{ "nodes": [ { "id": "bounds_s5", "type": "analytical_bounds", "inputs": { "size": 5, "lower_bound": 0.36, "upper_bound": 0.6 }, "result": { "lower": 0.36, "upper": 0.6 }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4632814 }, { "id": "bounds_s6", "type": "analytical_bounds", "inputs": { "size": 6, "lower_bound": 0.3056, "upper_bound": 0.5833 }, "result": { "lower": 0.3056, "upper": 0.5833 }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4632938 }, { "id": "bounds_s7", "type": "analytical_bounds", "inputs": { "size": 7, "lower_bound": 0.2653, "upper_bound": 0.5714 }, "result": { "lower": 0.2653, "upper": 0.5714 }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4632998 }, { "id": "bounds_s8", "type": "analytical_bounds", "inputs": { "size": 8, "lower_bound": 0.2344, "upper_bound": 0.5625 }, "result": { "lower": 0.2344, "upper": 0.5625 }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4633026 }, { "id": "bounds_s10", "type": "analytical_bounds", "inputs": { "size": 10, "lower_bound": 0.19, "upper_bound": 0.55 }, "result": { "lower": 0.19, "upper": 0.55 }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4633055 }, { "id": "sidon_pow2_s5", "type": "reference", "inputs": { "type": "sidon_pow2", "size": 5, "labels": [ 1, 2, 4, 8, 16 ] }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 15, "sidon_score": 0.6, "max_degeneracy": 2, "collision_count": 10, "collision_entropy": 3.8439, "collision_histogram": { "3": 2, "5": 2, "9": 2, "17": 2, "6": 2, "10": 2, "18": 2, "12": 2, "20": 2, "24": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.463362 }, { "id": "nonsidon_seq_s5", "type": "reference", "inputs": { "type": "nonsidon_consecutive", "size": 5, "labels": [ 1, 2, 3, 4, 5 ] }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 9, "sidon_score": 0.36, "max_degeneracy": 5, "collision_count": 7, "collision_entropy": 2.9991, "collision_histogram": { "3": 2, "4": 3, "5": 4, "6": 5, "7": 4, "8": 3, "9": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.463386 }, { "id": "sidon_pow2_s6", "type": "reference", "inputs": { "type": "sidon_pow2", "size": 6, "labels": [ 1, 2, 4, 8, 16, 32 ] }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 21, "sidon_score": 0.583333, "max_degeneracy": 2, "collision_count": 15, "collision_entropy": 4.3366, "collision_histogram": { "3": 2, "5": 2, "9": 2, "17": 2, "33": 2, "6": 2, "10": 2, "18": 2, "34": 2, "12": 2, "20": 2, "36": 2, "24": 2, "40": 2, "48": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.463407 }, { "id": "nonsidon_seq_s6", "type": "reference", "inputs": { "type": "nonsidon_consecutive", "size": 6, "labels": [ 1, 2, 3, 4, 5, 6 ] }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 11, "sidon_score": 0.305556, "max_degeneracy": 6, "collision_count": 9, "collision_entropy": 3.2744, "collision_histogram": { "3": 2, "4": 3, "5": 4, "6": 5, "7": 6, "8": 5, "9": 4, "10": 3, "11": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4634237 }, { "id": "sidon_pow2_s7", "type": "reference", "inputs": { "type": "sidon_pow2", "size": 7, "labels": [ 1, 2, 4, 8, 16, 32, 64 ] }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 28, "sidon_score": 0.571429, "max_degeneracy": 2, "collision_count": 21, "collision_entropy": 4.7576, "collision_histogram": { "3": 2, "5": 2, "9": 2, "17": 2, "33": 2, "65": 2, "6": 2, "10": 2, "18": 2, "34": 2, "66": 2, "12": 2, "20": 2, "36": 2, "68": 2, "24": 2, "40": 2, "72": 2, "48": 2, "80": 2, "96": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.463446 }, { "id": "nonsidon_seq_s7", "type": "reference", "inputs": { "type": "nonsidon_consecutive", "size": 7, "labels": [ 1, 2, 3, 4, 5, 6, 7 ] }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 13, "sidon_score": 0.265306, "max_degeneracy": 7, "collision_count": 11, "collision_entropy": 3.5045, "collision_histogram": { "3": 2, "4": 3, "5": 4, "6": 5, "7": 6, "8": 7, "9": 6, "10": 5, "11": 4, "12": 3, "13": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4634626 }, { "id": "sidon_pow2_s8", "type": "reference", "inputs": { "type": "sidon_pow2", "size": 8, "labels": [ 1, 2, 4, 8, 16, 32, 64, 128 ] }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 36, "sidon_score": 0.5625, "max_degeneracy": 2, "collision_count": 28, "collision_entropy": 5.125, "collision_histogram": { "3": 2, "5": 2, "9": 2, "17": 2, "33": 2, "65": 2, "129": 2, "6": 2, "10": 2, "18": 2, "34": 2, "66": 2, "130": 2, "12": 2, "20": 2, "36": 2, "68": 2, "132": 2, "24": 2, "40": 2, "72": 2, "136": 2, "48": 2, "80": 2, "144": 2, "96": 2, "160": 2, "192": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.463489 }, { "id": "nonsidon_seq_s8", "type": "reference", "inputs": { "type": "nonsidon_consecutive", "size": 8, "labels": [ 1, 2, 3, 4, 5, 6, 7, 8 ] }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 15, "sidon_score": 0.234375, "max_degeneracy": 8, "collision_count": 13, "collision_entropy": 3.7023, "collision_histogram": { "3": 2, "4": 3, "5": 4, "6": 5, "7": 6, "8": 7, "9": 8, "10": 7, "11": 6, "12": 5, "13": 4, "14": 3, "15": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4635081 }, { "id": "sidon_pow2_s10", "type": "reference", "inputs": { "type": "sidon_pow2", "size": 10, "labels": [ 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ] }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 55, "sidon_score": 0.55, "max_degeneracy": 2, "collision_count": 45, "collision_entropy": 5.7439, "collision_histogram": { "3": 2, "5": 2, "9": 2, "17": 2, "33": 2, "65": 2, "129": 2, "257": 2, "513": 2, "6": 2, "10": 2, "18": 2, "34": 2, "66": 2, "130": 2, "258": 2, "514": 2, "12": 2, "20": 2, "36": 2, "68": 2, "132": 2, "260": 2, "516": 2, "24": 2, "40": 2, "72": 2, "136": 2, "264": 2, "520": 2, "48": 2, "80": 2, "144": 2, "272": 2, "528": 2, "96": 2, "160": 2, "288": 2, "544": 2, "192": 2, "320": 2, "576": 2, "384": 2, "640": 2, "768": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4635487 }, { "id": "nonsidon_seq_s10", "type": "reference", "inputs": { "type": "nonsidon_consecutive", "size": 10, "labels": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 19, "sidon_score": 0.19, "max_degeneracy": 10, "collision_count": 17, "collision_entropy": 4.0306, "collision_histogram": { "3": 2, "4": 3, "5": 4, "6": 5, "7": 6, "8": 7, "9": 8, "10": 9, "11": 10, "12": 9, "13": 8, "14": 7, "15": 6, "16": 5, "17": 4, "18": 3, "19": 2 } }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120468.4635704 }, { "id": "primes_small_s5", "type": "prime_set", "inputs": { "size": 5, "scale": "small", "labels": [ 2, 3, 5, 7, 11 ], "range": [ 2, 11 ], "null_trials": 1000 }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 13, "sidon_score": 0.52, "max_degeneracy": 3, "collision_count": 10, "collision_entropy": 3.6235, "collision_histogram": { "5": 2, "7": 2, "9": 2, "13": 2, "8": 2, "10": 3, "14": 3, "12": 2, "16": 2, "18": 2 }, "null_distribution": { "mean": 0.4881, "std": 0.0442, "p5": 0.4, "p50": 0.48, "p95": 0.56, "trials": 1000 }, "p_value_two_sided": 0.806, "effect_size": 0.0319, "significant": false }, "status": "success", "elapsed_s": 0.0297, "timestamp": 1783120468.8049326 }, { "id": "primes_small_s6", "type": "prime_set", "inputs": { "size": 6, "scale": "small", "labels": [ 2, 3, 5, 7, 11, 13 ], "range": [ 2, 13 ], "null_trials": 1000 }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 17, "sidon_score": 0.472222, "max_degeneracy": 4, "collision_count": 13, "collision_entropy": 3.9613, "collision_histogram": { "5": 2, "7": 2, "9": 2, "13": 2, "15": 2, "8": 2, "10": 3, "14": 3, "16": 4, "12": 2, "18": 4, "20": 2, "24": 2 }, "null_distribution": { "mean": 0.4369, "std": 0.0408, "p5": 0.3611, "p50": 0.4444, "p95": 0.5, "trials": 1000 }, "p_value_two_sided": 0.668, "effect_size": 0.0353, "significant": false }, "status": "success", "elapsed_s": 0.0344, "timestamp": 1783120469.1452806 }, { "id": "primes_small_s7", "type": "prime_set", "inputs": { "size": 7, "scale": "small", "labels": [ 2, 3, 5, 7, 11, 13, 17 ], "range": [ 2, 17 ], "null_trials": 1000 }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 21, "sidon_score": 0.428571, "max_degeneracy": 4, "collision_count": 17, "collision_entropy": 4.2624, "collision_histogram": { "5": 2, "7": 2, "9": 2, "13": 2, "15": 2, "19": 2, "8": 2, "10": 3, "14": 3, "16": 4, "20": 4, "12": 2, "18": 4, "22": 3, "24": 4, "28": 2, "30": 2 }, "null_distribution": { "mean": 0.4191, "std": 0.0352, "p5": 0.3673, "p50": 0.4286, "p95": 0.4694, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0095, "significant": false }, "status": "success", "elapsed_s": 0.0411, "timestamp": 1783120469.4886904 }, { "id": "primes_small_s8", "type": "prime_set", "inputs": { "size": 8, "scale": "small", "labels": [ 2, 3, 5, 7, 11, 13, 17, 19 ], "range": [ 2, 19 ], "null_trials": 1000 }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 25, "sidon_score": 0.390625, "max_degeneracy": 6, "collision_count": 21, "collision_entropy": 4.4784, "collision_histogram": { "5": 2, "7": 2, "9": 2, "13": 2, "15": 2, "19": 2, "21": 2, "8": 2, "10": 3, "14": 3, "16": 4, "20": 4, "22": 5, "12": 2, "18": 4, "24": 6, "26": 3, "28": 2, "30": 4, "32": 2, "36": 2 }, "null_distribution": { "mean": 0.3822, "std": 0.0326, "p5": 0.3281, "p50": 0.3906, "p95": 0.4375, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0084, "significant": false }, "status": "success", "elapsed_s": 0.0475, "timestamp": 1783120469.8475132 }, { "id": "primes_small_s10", "type": "prime_set", "inputs": { "size": 10, "scale": "small", "labels": [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ], "range": [ 2, 29 ], "null_trials": 1000 }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 33, "sidon_score": 0.33, "max_degeneracy": 6, "collision_count": 29, "collision_entropy": 4.8676, "collision_histogram": { "5": 2, "7": 2, "9": 2, "13": 2, "15": 2, "19": 2, "21": 2, "25": 2, "31": 2, "8": 2, "10": 3, "14": 3, "16": 4, "20": 4, "22": 5, "26": 5, "32": 4, "12": 2, "18": 4, "24": 6, "28": 4, "34": 5, "30": 6, "36": 6, "40": 4, "42": 4, "46": 3, "48": 2, "52": 2 }, "null_distribution": { "mean": 0.365, "std": 0.0275, "p5": 0.32, "p50": 0.37, "p95": 0.41, "trials": 1000 }, "p_value_two_sided": 0.298, "effect_size": -0.035, "significant": false }, "status": "success", "elapsed_s": 0.0636, "timestamp": 1783120470.213078 }, { "id": "primes_kilo_s5", "type": "prime_set", "inputs": { "size": 5, "scale": "kilo", "labels": [ 1009, 1013, 1019, 1021, 1031 ], "range": [ 1009, 1031 ], "null_trials": 1000 }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 14, "sidon_score": 0.56, "max_degeneracy": 4, "collision_count": 9, "collision_entropy": 3.6839, "collision_histogram": { "2022": 2, "2028": 2, "2030": 2, "2040": 4, "2032": 2, "2034": 2, "2044": 2, "2050": 2, "2052": 2 }, "null_distribution": { "mean": 0.5537, "std": 0.0359, "p5": 0.48, "p50": 0.56, "p95": 0.6, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0063, "significant": false }, "status": "success", "elapsed_s": 0.0322, "timestamp": 1783120470.5489564 }, { "id": "primes_kilo_s6", "type": "prime_set", "inputs": { "size": 6, "scale": "kilo", "labels": [ 1009, 1013, 1019, 1021, 1031, 1033 ], "range": [ 1009, 1033 ], "null_trials": 1000 }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 18, "sidon_score": 0.5, "max_degeneracy": 4, "collision_count": 13, "collision_entropy": 4.0378, "collision_histogram": { "2022": 2, "2028": 2, "2030": 2, "2040": 4, "2042": 3, "2032": 2, "2034": 2, "2044": 2, "2046": 2, "2050": 2, "2052": 4, "2054": 2, "2064": 2 }, "null_distribution": { "mean": 0.516, "std": 0.0336, "p5": 0.4444, "p50": 0.5278, "p95": 0.5556, "trials": 1000 }, "p_value_two_sided": 0.844, "effect_size": -0.016, "significant": false }, "status": "success", "elapsed_s": 0.0415, "timestamp": 1783120470.8916674 }, { "id": "primes_kilo_s7", "type": "prime_set", "inputs": { "size": 7, "scale": "kilo", "labels": [ 1009, 1013, 1019, 1021, 1031, 1033, 1039 ], "range": [ 1009, 1039 ], "null_trials": 1000 }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 24, "sidon_score": 0.489796, "max_degeneracy": 6, "collision_count": 18, "collision_entropy": 4.4256, "collision_histogram": { "2022": 2, "2028": 2, "2030": 2, "2040": 4, "2042": 3, "2048": 2, "2032": 2, "2034": 2, "2044": 2, "2046": 2, "2052": 6, "2050": 2, "2058": 2, "2054": 2, "2060": 2, "2064": 2, "2070": 2, "2072": 2 }, "null_distribution": { "mean": 0.4912, "std": 0.0336, "p5": 0.4286, "p50": 0.4898, "p95": 0.5306, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": -0.0014, "significant": false }, "status": "success", "elapsed_s": 0.0479, "timestamp": 1783120471.2387857 }, { "id": "primes_kilo_s8", "type": "prime_set", "inputs": { "size": 8, "scale": "kilo", "labels": [ 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049 ], "range": [ 1009, 1049 ], "null_trials": 1000 }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 29, "sidon_score": 0.453125, "max_degeneracy": 6, "collision_count": 23, "collision_entropy": 4.7028, "collision_histogram": { "2022": 2, "2028": 2, "2030": 2, "2040": 4, "2042": 3, "2048": 2, "2058": 4, "2032": 2, "2034": 2, "2044": 2, "2046": 2, "2052": 6, "2062": 3, "2050": 2, "2068": 2, "2054": 2, "2060": 2, "2070": 4, "2064": 2, "2080": 2, "2072": 2, "2082": 2, "2088": 2 }, "null_distribution": { "mean": 0.4793, "std": 0.0286, "p5": 0.4375, "p50": 0.4844, "p95": 0.5156, "trials": 1000 }, "p_value_two_sided": 0.502, "effect_size": -0.0262, "significant": false }, "status": "success", "elapsed_s": 0.0576, "timestamp": 1783120471.5968723 }, { "id": "primes_kilo_s10", "type": "prime_set", "inputs": { "size": 10, "scale": "kilo", "labels": [ 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061 ], "range": [ 1009, 1061 ], "null_trials": 1000 }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 39, "sidon_score": 0.39, "max_degeneracy": 8, "collision_count": 31, "collision_entropy": 5.0586, "collision_histogram": { "2022": 2, "2028": 2, "2030": 2, "2040": 4, "2042": 3, "2048": 2, "2058": 4, "2060": 4, "2070": 8, "2032": 2, "2034": 2, "2044": 2, "2046": 2, "2052": 6, "2062": 3, "2064": 4, "2074": 2, "2050": 2, "2068": 2, "2080": 4, "2054": 2, "2072": 4, "2082": 6, "2092": 2, "2084": 2, "2094": 2, "2088": 2, "2090": 2, "2100": 4, "2110": 2, "2112": 2 }, "null_distribution": { "mean": 0.4461, "std": 0.0256, "p5": 0.4, "p50": 0.45, "p95": 0.48, "trials": 1000 }, "p_value_two_sided": 0.104, "effect_size": -0.0561, "significant": false }, "status": "success", "elapsed_s": 0.0795, "timestamp": 1783120471.9800327 }, { "id": "primes_million_s5", "type": "prime_set", "inputs": { "size": 5, "scale": "million", "labels": [ 1000003, 1000033, 1000037, 1000039, 1000081 ], "range": [ 1000003, 1000081 ], "null_trials": 1000 }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 15, "sidon_score": 0.6, "max_degeneracy": 2, "collision_count": 10, "collision_entropy": 3.8439, "collision_histogram": { "2000036": 2, "2000040": 2, "2000042": 2, "2000084": 2, "2000070": 2, "2000072": 2, "2000114": 2, "2000076": 2, "2000118": 2, "2000120": 2 }, "null_distribution": { "mean": 0.5878, "std": 0.02, "p5": 0.56, "p50": 0.6, "p95": 0.6, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0122, "significant": false }, "status": "success", "elapsed_s": 0.0347, "timestamp": 1783120472.3185062 }, { "id": "primes_million_s6", "type": "prime_set", "inputs": { "size": 6, "scale": "million", "labels": [ 1000003, 1000033, 1000037, 1000039, 1000081, 1000099 ], "range": [ 1000003, 1000099 ], "null_trials": 1000 }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 21, "sidon_score": 0.583333, "max_degeneracy": 2, "collision_count": 15, "collision_entropy": 4.3366, "collision_histogram": { "2000036": 2, "2000040": 2, "2000042": 2, "2000084": 2, "2000102": 2, "2000070": 2, "2000072": 2, "2000114": 2, "2000132": 2, "2000076": 2, "2000118": 2, "2000136": 2, "2000120": 2, "2000138": 2, "2000180": 2 }, "null_distribution": { "mean": 0.566, "std": 0.0203, "p5": 0.5278, "p50": 0.5556, "p95": 0.5833, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0173, "significant": false }, "status": "success", "elapsed_s": 0.0411, "timestamp": 1783120472.6634493 }, { "id": "primes_million_s7", "type": "prime_set", "inputs": { "size": 7, "scale": "million", "labels": [ 1000003, 1000033, 1000037, 1000039, 1000081, 1000099, 1000117 ], "range": [ 1000003, 1000117 ], "null_trials": 1000 }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 26, "sidon_score": 0.530612, "max_degeneracy": 4, "collision_count": 20, "collision_entropy": 4.6197, "collision_histogram": { "2000036": 2, "2000040": 2, "2000042": 2, "2000084": 2, "2000102": 2, "2000120": 4, "2000070": 2, "2000072": 2, "2000114": 2, "2000132": 2, "2000150": 2, "2000076": 2, "2000118": 2, "2000136": 2, "2000154": 2, "2000138": 2, "2000156": 2, "2000180": 2, "2000198": 3, "2000216": 2 }, "null_distribution": { "mean": 0.5495, "std": 0.0207, "p5": 0.5102, "p50": 0.551, "p95": 0.5714, "trials": 1000 }, "p_value_two_sided": 0.492, "effect_size": -0.0189, "significant": false }, "status": "success", "elapsed_s": 0.0512, "timestamp": 1783120473.031353 }, { "id": "primes_million_s8", "type": "prime_set", "inputs": { "size": 8, "scale": "million", "labels": [ 1000003, 1000033, 1000037, 1000039, 1000081, 1000099, 1000117, 1000121 ], "range": [ 1000003, 1000121 ], "null_trials": 1000 }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 33, "sidon_score": 0.515625, "max_degeneracy": 4, "collision_count": 26, "collision_entropy": 4.957, "collision_histogram": { "2000036": 2, "2000040": 2, "2000042": 2, "2000084": 2, "2000102": 2, "2000120": 4, "2000124": 2, "2000070": 2, "2000072": 2, "2000114": 2, "2000132": 2, "2000150": 2, "2000154": 4, "2000076": 2, "2000118": 2, "2000136": 2, "2000158": 2, "2000138": 2, "2000156": 2, "2000160": 2, "2000180": 2, "2000198": 3, "2000202": 2, "2000216": 2, "2000220": 2, "2000238": 2 }, "null_distribution": { "mean": 0.5343, "std": 0.0202, "p5": 0.5, "p50": 0.5312, "p95": 0.5625, "trials": 1000 }, "p_value_two_sided": 0.504, "effect_size": -0.0187, "significant": false }, "status": "success", "elapsed_s": 0.0603, "timestamp": 1783120473.4020586 }, { "id": "primes_million_s10", "type": "prime_set", "inputs": { "size": 10, "scale": "million", "labels": [ 1000003, 1000033, 1000037, 1000039, 1000081, 1000099, 1000117, 1000121, 1000133, 1000151 ], "range": [ 1000003, 1000151 ], "null_trials": 1000 }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 48, "sidon_score": 0.48, "max_degeneracy": 6, "collision_count": 39, "collision_entropy": 5.4612, "collision_histogram": { "2000036": 2, "2000040": 2, "2000042": 2, "2000084": 2, "2000102": 2, "2000120": 4, "2000124": 2, "2000136": 4, "2000154": 6, "2000070": 2, "2000072": 2, "2000114": 2, "2000132": 2, "2000150": 2, "2000166": 2, "2000184": 2, "2000076": 2, "2000118": 2, "2000158": 2, "2000170": 2, "2000188": 2, "2000138": 2, "2000156": 2, "2000160": 2, "2000172": 2, "2000190": 2, "2000180": 2, "2000198": 3, "2000202": 2, "2000214": 2, "2000232": 4, "2000216": 2, "2000220": 2, "2000250": 4, "2000238": 2, "2000268": 2, "2000254": 2, "2000272": 2, "2000284": 2 }, "null_distribution": { "mean": 0.5106, "std": 0.0181, "p5": 0.48, "p50": 0.51, "p95": 0.54, "trials": 1000 }, "p_value_two_sided": 0.16, "effect_size": -0.0306, "significant": false }, "status": "success", "elapsed_s": 0.0822, "timestamp": 1783120473.7883615 }, { "id": "primes_billion_s5", "type": "prime_set", "inputs": { "size": 5, "scale": "billion", "labels": [ 1000000007, 1000000009, 1000000021, 1000000033, 1000000087 ], "range": [ 1000000007, 1000000087 ], "null_trials": 1000 }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 14, "sidon_score": 0.56, "max_degeneracy": 3, "collision_count": 10, "collision_entropy": 3.7337, "collision_histogram": { "2000000016": 2, "2000000028": 2, "2000000040": 2, "2000000094": 2, "2000000030": 2, "2000000042": 3, "2000000096": 2, "2000000054": 2, "2000000108": 2, "2000000120": 2 }, "null_distribution": { "mean": 0.5868, "std": 0.0225, "p5": 0.56, "p50": 0.6, "p95": 0.6, "trials": 1000 }, "p_value_two_sided": 0.502, "effect_size": -0.0268, "significant": false }, "status": "success", "elapsed_s": 0.0347, "timestamp": 1783120474.0052655 }, { "id": "primes_billion_s6", "type": "prime_set", "inputs": { "size": 6, "scale": "billion", "labels": [ 1000000007, 1000000009, 1000000021, 1000000033, 1000000087, 1000000093 ], "range": [ 1000000007, 1000000093 ], "null_trials": 1000 }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 20, "sidon_score": 0.555556, "max_degeneracy": 3, "collision_count": 15, "collision_entropy": 4.2601, "collision_histogram": { "2000000016": 2, "2000000028": 2, "2000000040": 2, "2000000094": 2, "2000000100": 2, "2000000030": 2, "2000000042": 3, "2000000096": 2, "2000000102": 2, "2000000054": 2, "2000000108": 2, "2000000114": 2, "2000000120": 2, "2000000126": 2, "2000000180": 2 }, "null_distribution": { "mean": 0.5644, "std": 0.0216, "p5": 0.5278, "p50": 0.5556, "p95": 0.5833, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": -0.0088, "significant": false }, "status": "success", "elapsed_s": 0.0431, "timestamp": 1783120474.0484068 }, { "id": "primes_billion_s7", "type": "prime_set", "inputs": { "size": 7, "scale": "billion", "labels": [ 1000000007, 1000000009, 1000000021, 1000000033, 1000000087, 1000000093, 1000000097 ], "range": [ 1000000007, 1000000097 ], "null_trials": 1000 }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 27, "sidon_score": 0.55102, "max_degeneracy": 3, "collision_count": 21, "collision_entropy": 4.7013, "collision_histogram": { "2000000016": 2, "2000000028": 2, "2000000040": 2, "2000000094": 2, "2000000100": 2, "2000000104": 2, "2000000030": 2, "2000000042": 3, "2000000096": 2, "2000000102": 2, "2000000106": 2, "2000000054": 2, "2000000108": 2, "2000000114": 2, "2000000118": 2, "2000000120": 2, "2000000126": 2, "2000000130": 2, "2000000180": 2, "2000000184": 2, "2000000190": 2 }, "null_distribution": { "mean": 0.5433, "std": 0.0224, "p5": 0.5102, "p50": 0.551, "p95": 0.5714, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0077, "significant": false }, "status": "success", "elapsed_s": 0.0512, "timestamp": 1783120474.0996733 }, { "id": "primes_billion_s8", "type": "prime_set", "inputs": { "size": 8, "scale": "billion", "labels": [ 1000000007, 1000000009, 1000000021, 1000000033, 1000000087, 1000000093, 1000000097, 1000000103 ], "range": [ 1000000007, 1000000103 ], "null_trials": 1000 }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 34, "sidon_score": 0.53125, "max_degeneracy": 4, "collision_count": 27, "collision_entropy": 5.0195, "collision_histogram": { "2000000016": 2, "2000000028": 2, "2000000040": 2, "2000000094": 2, "2000000100": 2, "2000000104": 2, "2000000110": 2, "2000000030": 2, "2000000042": 3, "2000000096": 2, "2000000102": 2, "2000000106": 2, "2000000112": 2, "2000000054": 2, "2000000108": 2, "2000000114": 2, "2000000118": 2, "2000000124": 2, "2000000120": 2, "2000000126": 2, "2000000130": 2, "2000000136": 2, "2000000180": 2, "2000000184": 2, "2000000190": 4, "2000000196": 2, "2000000200": 2 }, "null_distribution": { "mean": 0.5268, "std": 0.0211, "p5": 0.4844, "p50": 0.5312, "p95": 0.5625, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0044, "significant": false }, "status": "success", "elapsed_s": 0.0608, "timestamp": 1783120474.160529 }, { "id": "primes_billion_s10", "type": "prime_set", "inputs": { "size": 10, "scale": "billion", "labels": [ 1000000007, 1000000009, 1000000021, 1000000033, 1000000087, 1000000093, 1000000097, 1000000103, 1000000123, 1000000181 ], "range": [ 1000000007, 1000000181 ], "null_trials": 1000 }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 51, "sidon_score": 0.51, "max_degeneracy": 6, "collision_count": 42, "collision_entropy": 5.5812, "collision_histogram": { "2000000016": 2, "2000000028": 2, "2000000040": 2, "2000000094": 2, "2000000100": 2, "2000000104": 2, "2000000110": 2, "2000000130": 4, "2000000188": 2, "2000000030": 2, "2000000042": 3, "2000000096": 2, "2000000102": 2, "2000000106": 2, "2000000112": 2, "2000000132": 2, "2000000190": 6, "2000000054": 2, "2000000108": 2, "2000000114": 2, "2000000118": 2, "2000000124": 2, "2000000144": 2, "2000000202": 2, "2000000120": 2, "2000000126": 2, "2000000136": 2, "2000000156": 2, "2000000214": 2, "2000000180": 2, "2000000184": 2, "2000000210": 2, "2000000268": 2, "2000000196": 2, "2000000216": 2, "2000000274": 2, "2000000200": 2, "2000000220": 2, "2000000278": 2, "2000000226": 2, "2000000284": 2, "2000000304": 2 }, "null_distribution": { "mean": 0.516, "std": 0.0171, "p5": 0.48, "p50": 0.52, "p95": 0.54, "trials": 1000 }, "p_value_two_sided": 0.82, "effect_size": -0.006, "significant": false }, "status": "success", "elapsed_s": 0.0843, "timestamp": 1783120474.2448404 }, { "id": "primes_trillion_s5", "type": "prime_set", "inputs": { "size": 5, "scale": "trillion", "labels": [ 1000000000039, 1000000000061, 1000000000063, 1000000000091, 1000000000121 ], "range": [ 1000000000039, 1000000000121 ], "null_trials": 1000 }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 14, "sidon_score": 0.56, "max_degeneracy": 3, "collision_count": 10, "collision_entropy": 3.7337, "collision_histogram": { "2000000000100": 2, "2000000000102": 2, "2000000000130": 2, "2000000000160": 2, "2000000000124": 2, "2000000000152": 2, "2000000000182": 3, "2000000000154": 2, "2000000000184": 2, "2000000000212": 2 }, "null_distribution": { "mean": 0.5895, "std": 0.0205, "p5": 0.56, "p50": 0.6, "p95": 0.6, "trials": 1000 }, "p_value_two_sided": 0.54, "effect_size": -0.0295, "significant": false }, "status": "success", "elapsed_s": 0.0343, "timestamp": 1783120474.2791667 }, { "id": "primes_trillion_s6", "type": "prime_set", "inputs": { "size": 6, "scale": "trillion", "labels": [ 1000000000039, 1000000000061, 1000000000063, 1000000000091, 1000000000121, 1000000000163 ], "range": [ 1000000000039, 1000000000163 ], "null_trials": 1000 }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 20, "sidon_score": 0.555556, "max_degeneracy": 3, "collision_count": 15, "collision_entropy": 4.2601, "collision_histogram": { "2000000000100": 2, "2000000000102": 2, "2000000000130": 2, "2000000000160": 2, "2000000000202": 2, "2000000000124": 2, "2000000000152": 2, "2000000000182": 3, "2000000000224": 2, "2000000000154": 2, "2000000000184": 2, "2000000000226": 2, "2000000000212": 2, "2000000000254": 2, "2000000000284": 2 }, "null_distribution": { "mean": 0.57, "std": 0.019, "p5": 0.5278, "p50": 0.5833, "p95": 0.5833, "trials": 1000 }, "p_value_two_sided": 0.766, "effect_size": -0.0144, "significant": false }, "status": "success", "elapsed_s": 0.0423, "timestamp": 1783120474.3214636 }, { "id": "primes_trillion_s7", "type": "prime_set", "inputs": { "size": 7, "scale": "trillion", "labels": [ 1000000000039, 1000000000061, 1000000000063, 1000000000091, 1000000000121, 1000000000163, 1000000000169 ], "range": [ 1000000000039, 1000000000169 ], "null_trials": 1000 }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 27, "sidon_score": 0.55102, "max_degeneracy": 3, "collision_count": 21, "collision_entropy": 4.7013, "collision_histogram": { "2000000000100": 2, "2000000000102": 2, "2000000000130": 2, "2000000000160": 2, "2000000000202": 2, "2000000000208": 2, "2000000000124": 2, "2000000000152": 2, "2000000000182": 3, "2000000000224": 2, "2000000000230": 2, "2000000000154": 2, "2000000000184": 2, "2000000000226": 2, "2000000000232": 2, "2000000000212": 2, "2000000000254": 2, "2000000000260": 2, "2000000000284": 2, "2000000000290": 2, "2000000000332": 2 }, "null_distribution": { "mean": 0.5523, "std": 0.0193, "p5": 0.5102, "p50": 0.551, "p95": 0.5714, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": -0.0013, "significant": false }, "status": "success", "elapsed_s": 0.0515, "timestamp": 1783120474.3729565 }, { "id": "primes_trillion_s8", "type": "prime_set", "inputs": { "size": 8, "scale": "trillion", "labels": [ 1000000000039, 1000000000061, 1000000000063, 1000000000091, 1000000000121, 1000000000163, 1000000000169, 1000000000177 ], "range": [ 1000000000039, 1000000000177 ], "null_trials": 1000 }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 35, "sidon_score": 0.546875, "max_degeneracy": 3, "collision_count": 28, "collision_entropy": 5.082, "collision_histogram": { "2000000000100": 2, "2000000000102": 2, "2000000000130": 2, "2000000000160": 2, "2000000000202": 2, "2000000000208": 2, "2000000000216": 2, "2000000000124": 2, "2000000000152": 2, "2000000000182": 3, "2000000000224": 2, "2000000000230": 2, "2000000000238": 2, "2000000000154": 2, "2000000000184": 2, "2000000000226": 2, "2000000000232": 2, "2000000000240": 2, "2000000000212": 2, "2000000000254": 2, "2000000000260": 2, "2000000000268": 2, "2000000000284": 2, "2000000000290": 2, "2000000000298": 2, "2000000000332": 2, "2000000000340": 2, "2000000000346": 2 }, "null_distribution": { "mean": 0.5374, "std": 0.0181, "p5": 0.5, "p50": 0.5469, "p95": 0.5625, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0095, "significant": false }, "status": "success", "elapsed_s": 0.0614, "timestamp": 1783120474.4343703 }, { "id": "primes_trillion_s10", "type": "prime_set", "inputs": { "size": 10, "scale": "trillion", "labels": [ 1000000000039, 1000000000061, 1000000000063, 1000000000091, 1000000000121, 1000000000163, 1000000000169, 1000000000177, 1000000000189, 1000000000193 ], "range": [ 1000000000039, 1000000000193 ], "null_trials": 1000 }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 51, "sidon_score": 0.51, "max_degeneracy": 4, "collision_count": 42, "collision_entropy": 5.5963, "collision_histogram": { "2000000000100": 2, "2000000000102": 2, "2000000000130": 2, "2000000000160": 2, "2000000000202": 2, "2000000000208": 2, "2000000000216": 2, "2000000000228": 2, "2000000000232": 4, "2000000000124": 2, "2000000000152": 2, "2000000000182": 3, "2000000000224": 2, "2000000000230": 2, "2000000000238": 2, "2000000000250": 2, "2000000000254": 4, "2000000000154": 2, "2000000000184": 2, "2000000000226": 2, "2000000000240": 2, "2000000000252": 2, "2000000000256": 2, "2000000000212": 2, "2000000000260": 2, "2000000000268": 2, "2000000000280": 2, "2000000000284": 4, "2000000000290": 2, "2000000000298": 2, "2000000000310": 2, "2000000000314": 2, "2000000000332": 2, "2000000000340": 2, "2000000000352": 2, "2000000000356": 2, "2000000000346": 2, "2000000000358": 2, "2000000000362": 2, "2000000000366": 2, "2000000000370": 2, "2000000000382": 2 }, "null_distribution": { "mean": 0.5119, "std": 0.0177, "p5": 0.48, "p50": 0.51, "p95": 0.54, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": -0.0019, "significant": false }, "status": "success", "elapsed_s": 0.0864, "timestamp": 1783120474.5207705 }, { "id": "primes_quadrillion_s5", "type": "prime_set", "inputs": { "size": 5, "scale": "quadrillion", "labels": [ 1000000000000037, 1000000000000091, 1000000000000159, 1000000000000187, 1000000000000223 ], "range": [ 1000000000000037, 1000000000000223 ], "null_trials": 1000 }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 15, "sidon_score": 0.6, "max_degeneracy": 2, "collision_count": 10, "collision_entropy": 3.8439, "collision_histogram": { "2000000000000128": 2, "2000000000000196": 2, "2000000000000224": 2, "2000000000000260": 2, "2000000000000250": 2, "2000000000000278": 2, "2000000000000314": 2, "2000000000000346": 2, "2000000000000382": 2, "2000000000000410": 2 }, "null_distribution": { "mean": 0.5942, "std": 0.0151, "p5": 0.56, "p50": 0.6, "p95": 0.6, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0058, "significant": false }, "status": "success", "elapsed_s": 0.034, "timestamp": 1783120474.5547967 }, { "id": "primes_quadrillion_s6", "type": "prime_set", "inputs": { "size": 6, "scale": "quadrillion", "labels": [ 1000000000000037, 1000000000000091, 1000000000000159, 1000000000000187, 1000000000000223, 1000000000000241 ], "range": [ 1000000000000037, 1000000000000241 ], "null_trials": 1000 }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 20, "sidon_score": 0.555556, "max_degeneracy": 4, "collision_count": 14, "collision_entropy": 4.2255, "collision_histogram": { "2000000000000128": 2, "2000000000000196": 2, "2000000000000224": 2, "2000000000000260": 2, "2000000000000278": 4, "2000000000000250": 2, "2000000000000314": 2, "2000000000000332": 2, "2000000000000346": 2, "2000000000000382": 2, "2000000000000400": 2, "2000000000000410": 2, "2000000000000428": 2, "2000000000000464": 2 }, "null_distribution": { "mean": 0.5748, "std": 0.0149, "p5": 0.5556, "p50": 0.5833, "p95": 0.5833, "trials": 1000 }, "p_value_two_sided": 0.524, "effect_size": -0.0192, "significant": false }, "status": "success", "elapsed_s": 0.0424, "timestamp": 1783120474.5972607 }, { "id": "primes_quadrillion_s7", "type": "prime_set", "inputs": { "size": 7, "scale": "quadrillion", "labels": [ 1000000000000037, 1000000000000091, 1000000000000159, 1000000000000187, 1000000000000223, 1000000000000241, 1000000000000249 ], "range": [ 1000000000000037, 1000000000000249 ], "null_trials": 1000 }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 27, "sidon_score": 0.55102, "max_degeneracy": 4, "collision_count": 20, "collision_entropy": 4.6759, "collision_histogram": { "2000000000000128": 2, "2000000000000196": 2, "2000000000000224": 2, "2000000000000260": 2, "2000000000000278": 4, "2000000000000286": 2, "2000000000000250": 2, "2000000000000314": 2, "2000000000000332": 2, "2000000000000340": 2, "2000000000000346": 2, "2000000000000382": 2, "2000000000000400": 2, "2000000000000408": 2, "2000000000000410": 2, "2000000000000428": 2, "2000000000000436": 2, "2000000000000464": 2, "2000000000000472": 2, "2000000000000490": 2 }, "null_distribution": { "mean": 0.5602, "std": 0.0149, "p5": 0.5306, "p50": 0.5714, "p95": 0.5714, "trials": 1000 }, "p_value_two_sided": 0.854, "effect_size": -0.0092, "significant": false }, "status": "success", "elapsed_s": 0.0512, "timestamp": 1783120474.6484785 }, { "id": "primes_quadrillion_s8", "type": "prime_set", "inputs": { "size": 8, "scale": "quadrillion", "labels": [ 1000000000000037, 1000000000000091, 1000000000000159, 1000000000000187, 1000000000000223, 1000000000000241, 1000000000000249, 1000000000000259 ], "range": [ 1000000000000037, 1000000000000259 ], "null_trials": 1000 }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 33, "sidon_score": 0.515625, "max_degeneracy": 4, "collision_count": 27, "collision_entropy": 4.9764, "collision_histogram": { "2000000000000128": 2, "2000000000000196": 2, "2000000000000224": 2, "2000000000000260": 2, "2000000000000278": 4, "2000000000000286": 2, "2000000000000296": 2, "2000000000000250": 2, "2000000000000314": 2, "2000000000000332": 2, "2000000000000340": 2, "2000000000000350": 2, "2000000000000346": 2, "2000000000000382": 2, "2000000000000400": 2, "2000000000000408": 2, "2000000000000418": 2, "2000000000000410": 2, "2000000000000428": 2, "2000000000000436": 2, "2000000000000446": 3, "2000000000000464": 2, "2000000000000472": 2, "2000000000000482": 3, "2000000000000490": 2, "2000000000000500": 2, "2000000000000508": 2 }, "null_distribution": { "mean": 0.5469, "std": 0.015, "p5": 0.5156, "p50": 0.5469, "p95": 0.5625, "trials": 1000 }, "p_value_two_sided": 0.142, "effect_size": -0.0313, "significant": false }, "status": "success", "elapsed_s": 0.0624, "timestamp": 1783120474.710894 }, { "id": "primes_quadrillion_s10", "type": "prime_set", "inputs": { "size": 10, "scale": "quadrillion", "labels": [ 1000000000000037, 1000000000000091, 1000000000000159, 1000000000000187, 1000000000000223, 1000000000000241, 1000000000000249, 1000000000000259, 1000000000000273, 1000000000000279 ], "range": [ 1000000000000037, 1000000000000279 ], "null_trials": 1000 }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 52, "sidon_score": 0.52, "max_degeneracy": 4, "collision_count": 44, "collision_entropy": 5.6488, "collision_histogram": { "2000000000000128": 2, "2000000000000196": 2, "2000000000000224": 2, "2000000000000260": 2, "2000000000000278": 4, "2000000000000286": 2, "2000000000000296": 2, "2000000000000310": 2, "2000000000000316": 2, "2000000000000250": 2, "2000000000000314": 2, "2000000000000332": 2, "2000000000000340": 2, "2000000000000350": 2, "2000000000000364": 2, "2000000000000370": 2, "2000000000000346": 2, "2000000000000382": 2, "2000000000000400": 2, "2000000000000408": 2, "2000000000000418": 2, "2000000000000432": 2, "2000000000000438": 2, "2000000000000410": 2, "2000000000000428": 2, "2000000000000436": 2, "2000000000000446": 3, "2000000000000460": 2, "2000000000000466": 2, "2000000000000464": 2, "2000000000000472": 2, "2000000000000482": 3, "2000000000000496": 2, "2000000000000502": 2, "2000000000000490": 2, "2000000000000500": 2, "2000000000000514": 2, "2000000000000520": 2, "2000000000000508": 2, "2000000000000522": 2, "2000000000000528": 2, "2000000000000532": 2, "2000000000000538": 2, "2000000000000552": 2 }, "null_distribution": { "mean": 0.5257, "std": 0.0148, "p5": 0.5, "p50": 0.53, "p95": 0.55, "trials": 1000 }, "p_value_two_sided": 0.88, "effect_size": -0.0057, "significant": false }, "status": "success", "elapsed_s": 0.0868, "timestamp": 1783120474.7977076 }, { "id": "primes_quintillion_s5", "type": "prime_set", "inputs": { "size": 5, "scale": "quintillion", "labels": [ 1000000000000000003, 1000000000000000009, 1000000000000000031, 1000000000000000079, 1000000000000000177 ], "range": [ 1000000000000000003, 1000000000000000177 ], "null_trials": 1000 }, "result": { "n": 5, "total_pairs": 25, "distinct_sums": 15, "sidon_score": 0.6, "max_degeneracy": 2, "collision_count": 10, "collision_entropy": 3.8439, "collision_histogram": { "2000000000000000012": 2, "2000000000000000034": 2, "2000000000000000082": 2, "2000000000000000180": 2, "2000000000000000040": 2, "2000000000000000088": 2, "2000000000000000186": 2, "2000000000000000110": 2, "2000000000000000208": 2, "2000000000000000256": 2 }, "null_distribution": { "mean": 0.5948, "std": 0.0144, "p5": 0.56, "p50": 0.6, "p95": 0.6, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": 0.0052, "significant": false }, "status": "success", "elapsed_s": 0.0351, "timestamp": 1783120474.8328228 }, { "id": "primes_quintillion_s6", "type": "prime_set", "inputs": { "size": 6, "scale": "quintillion", "labels": [ 1000000000000000003, 1000000000000000009, 1000000000000000031, 1000000000000000079, 1000000000000000177, 1000000000000000183 ], "range": [ 1000000000000000003, 1000000000000000183 ], "null_trials": 1000 }, "result": { "n": 6, "total_pairs": 36, "distinct_sums": 20, "sidon_score": 0.555556, "max_degeneracy": 4, "collision_count": 14, "collision_entropy": 4.2255, "collision_histogram": { "2000000000000000012": 2, "2000000000000000034": 2, "2000000000000000082": 2, "2000000000000000180": 2, "2000000000000000186": 4, "2000000000000000040": 2, "2000000000000000088": 2, "2000000000000000192": 2, "2000000000000000110": 2, "2000000000000000208": 2, "2000000000000000214": 2, "2000000000000000256": 2, "2000000000000000262": 2, "2000000000000000360": 2 }, "null_distribution": { "mean": 0.5735, "std": 0.0159, "p5": 0.5556, "p50": 0.5833, "p95": 0.5833, "trials": 1000 }, "p_value_two_sided": 0.59, "effect_size": -0.0179, "significant": false }, "status": "success", "elapsed_s": 0.0441, "timestamp": 1783120474.8769648 }, { "id": "primes_quintillion_s7", "type": "prime_set", "inputs": { "size": 7, "scale": "quintillion", "labels": [ 1000000000000000003, 1000000000000000009, 1000000000000000031, 1000000000000000079, 1000000000000000177, 1000000000000000183, 1000000000000000201 ], "range": [ 1000000000000000003, 1000000000000000201 ], "null_trials": 1000 }, "result": { "n": 7, "total_pairs": 49, "distinct_sums": 27, "sidon_score": 0.55102, "max_degeneracy": 4, "collision_count": 20, "collision_entropy": 4.6759, "collision_histogram": { "2000000000000000012": 2, "2000000000000000034": 2, "2000000000000000082": 2, "2000000000000000180": 2, "2000000000000000186": 4, "2000000000000000204": 2, "2000000000000000040": 2, "2000000000000000088": 2, "2000000000000000192": 2, "2000000000000000210": 2, "2000000000000000110": 2, "2000000000000000208": 2, "2000000000000000214": 2, "2000000000000000232": 2, "2000000000000000256": 2, "2000000000000000262": 2, "2000000000000000280": 2, "2000000000000000360": 2, "2000000000000000378": 2, "2000000000000000384": 2 }, "null_distribution": { "mean": 0.5589, "std": 0.015, "p5": 0.5306, "p50": 0.5714, "p95": 0.5714, "trials": 1000 }, "p_value_two_sided": 0.958, "effect_size": -0.0079, "significant": false }, "status": "success", "elapsed_s": 0.0527, "timestamp": 1783120474.929676 }, { "id": "primes_quintillion_s8", "type": "prime_set", "inputs": { "size": 8, "scale": "quintillion", "labels": [ 1000000000000000003, 1000000000000000009, 1000000000000000031, 1000000000000000079, 1000000000000000177, 1000000000000000183, 1000000000000000201, 1000000000000000283 ], "range": [ 1000000000000000003, 1000000000000000283 ], "null_trials": 1000 }, "result": { "n": 8, "total_pairs": 64, "distinct_sums": 35, "sidon_score": 0.546875, "max_degeneracy": 4, "collision_count": 27, "collision_entropy": 5.0625, "collision_histogram": { "2000000000000000012": 2, "2000000000000000034": 2, "2000000000000000082": 2, "2000000000000000180": 2, "2000000000000000186": 4, "2000000000000000204": 2, "2000000000000000286": 2, "2000000000000000040": 2, "2000000000000000088": 2, "2000000000000000192": 2, "2000000000000000210": 2, "2000000000000000292": 2, "2000000000000000110": 2, "2000000000000000208": 2, "2000000000000000214": 2, "2000000000000000232": 2, "2000000000000000314": 2, "2000000000000000256": 2, "2000000000000000262": 2, "2000000000000000280": 2, "2000000000000000362": 2, "2000000000000000360": 2, "2000000000000000378": 2, "2000000000000000460": 2, "2000000000000000384": 2, "2000000000000000466": 2, "2000000000000000484": 2 }, "null_distribution": { "mean": 0.5497, "std": 0.014, "p5": 0.5312, "p50": 0.5469, "p95": 0.5625, "trials": 1000 }, "p_value_two_sided": 1.0, "effect_size": -0.0028, "significant": false }, "status": "success", "elapsed_s": 0.0646, "timestamp": 1783120474.9943037 }, { "id": "primes_quintillion_s10", "type": "prime_set", "inputs": { "size": 10, "scale": "quintillion", "labels": [ 1000000000000000003, 1000000000000000009, 1000000000000000031, 1000000000000000079, 1000000000000000177, 1000000000000000183, 1000000000000000201, 1000000000000000283, 1000000000000000381, 1000000000000000387 ], "range": [ 1000000000000000003, 1000000000000000387 ], "null_trials": 1000 }, "result": { "n": 10, "total_pairs": 100, "distinct_sums": 49, "sidon_score": 0.49, "max_degeneracy": 4, "collision_count": 39, "collision_entropy": 5.5039, "collision_histogram": { "2000000000000000012": 2, "2000000000000000034": 2, "2000000000000000082": 2, "2000000000000000180": 2, "2000000000000000186": 4, "2000000000000000204": 2, "2000000000000000286": 2, "2000000000000000384": 4, "2000000000000000390": 4, "2000000000000000040": 2, "2000000000000000088": 2, "2000000000000000192": 2, "2000000000000000210": 2, "2000000000000000292": 2, "2000000000000000396": 2, "2000000000000000110": 2, "2000000000000000208": 2, "2000000000000000214": 2, "2000000000000000232": 2, "2000000000000000314": 2, "2000000000000000412": 2, "2000000000000000418": 2, "2000000000000000256": 2, "2000000000000000262": 2, "2000000000000000280": 2, "2000000000000000362": 2, "2000000000000000460": 4, "2000000000000000466": 4, "2000000000000000360": 2, "2000000000000000378": 2, "2000000000000000558": 2, "2000000000000000564": 4, "2000000000000000570": 2, "2000000000000000484": 2, "2000000000000000582": 2, "2000000000000000588": 2, "2000000000000000664": 2, "2000000000000000670": 2, "2000000000000000768": 2 }, "null_distribution": { "mean": 0.5353, "std": 0.012, "p5": 0.51, "p50": 0.54, "p95": 0.55, "trials": 1000 }, "p_value_two_sided": 0.008, "effect_size": -0.0453, "significant": true }, "status": "success", "elapsed_s": 0.0886, "timestamp": 1783120475.0829244 }, { "id": "summary", "type": "summary", "inputs": { "schema": "prime_sidon_explore_v2", "claim_boundary": "prime-sidon-vs-random-null:permutation-test", "config": { "sizes": [ 5, 6, 7, 8, 10 ], "scales": [ "small", "kilo", "million", "billion", "trillion", "quadrillion", "quintillion" ], "null_trials": 1000 }, "analysis": [ { "size": 5, "n_significant": 0, "n_total": 7, "all_significant": false, "negative_effects": 2, "positive_effects": 5, "score_trend_increasing": false, "scores_by_scale": { "small": 0.52, "kilo": 0.56, "million": 0.6, "billion": 0.56, "trillion": 0.56, "quadrillion": 0.6, "quintillion": 0.6 } }, { "size": 6, "n_significant": 0, "n_total": 7, "all_significant": false, "negative_effects": 5, "positive_effects": 2, "score_trend_increasing": false, "scores_by_scale": { "small": 0.472222, "kilo": 0.5, "million": 0.583333, "billion": 0.555556, "trillion": 0.555556, "quadrillion": 0.555556, "quintillion": 0.555556 } }, { "size": 7, "n_significant": 0, "n_total": 7, "all_significant": false, "negative_effects": 5, "positive_effects": 2, "score_trend_increasing": true, "scores_by_scale": { "small": 0.428571, "kilo": 0.489796, "million": 0.530612, "billion": 0.55102, "trillion": 0.55102, "quadrillion": 0.55102, "quintillion": 0.55102 } }, { "size": 8, "n_significant": 0, "n_total": 7, "all_significant": false, "negative_effects": 4, "positive_effects": 3, "score_trend_increasing": false, "scores_by_scale": { "small": 0.390625, "kilo": 0.453125, "million": 0.515625, "billion": 0.53125, "trillion": 0.546875, "quadrillion": 0.515625, "quintillion": 0.546875 } }, { "size": 10, "n_significant": 1, "n_total": 7, "all_significant": false, "negative_effects": 7, "positive_effects": 0, "score_trend_increasing": false, "scores_by_scale": { "small": 0.33, "kilo": 0.39, "million": 0.48, "billion": 0.51, "trillion": 0.51, "quadrillion": 0.52, "quintillion": 0.49 } } ], "total_test_cases": 35, "total_significant": 1 }, "result": { "schema": "prime_sidon_explore_v2", "claim_boundary": "prime-sidon-vs-random-null:permutation-test", "config": { "sizes": [ 5, 6, 7, 8, 10 ], "scales": [ "small", "kilo", "million", "billion", "trillion", "quadrillion", "quintillion" ], "null_trials": 1000 }, "analysis": [ { "size": 5, "n_significant": 0, "n_total": 7, "all_significant": false, "negative_effects": 2, "positive_effects": 5, "score_trend_increasing": false, "scores_by_scale": { "small": 0.52, "kilo": 0.56, "million": 0.6, "billion": 0.56, "trillion": 0.56, "quadrillion": 0.6, "quintillion": 0.6 } }, { "size": 6, "n_significant": 0, "n_total": 7, "all_significant": false, "negative_effects": 5, "positive_effects": 2, "score_trend_increasing": false, "scores_by_scale": { "small": 0.472222, "kilo": 0.5, "million": 0.583333, "billion": 0.555556, "trillion": 0.555556, "quadrillion": 0.555556, "quintillion": 0.555556 } }, { "size": 7, "n_significant": 0, "n_total": 7, "all_significant": false, "negative_effects": 5, "positive_effects": 2, "score_trend_increasing": true, "scores_by_scale": { "small": 0.428571, "kilo": 0.489796, "million": 0.530612, "billion": 0.55102, "trillion": 0.55102, "quadrillion": 0.55102, "quintillion": 0.55102 } }, { "size": 8, "n_significant": 0, "n_total": 7, "all_significant": false, "negative_effects": 4, "positive_effects": 3, "score_trend_increasing": false, "scores_by_scale": { "small": 0.390625, "kilo": 0.453125, "million": 0.515625, "billion": 0.53125, "trillion": 0.546875, "quadrillion": 0.515625, "quintillion": 0.546875 } }, { "size": 10, "n_significant": 1, "n_total": 7, "all_significant": false, "negative_effects": 7, "positive_effects": 0, "score_trend_increasing": false, "scores_by_scale": { "small": 0.33, "kilo": 0.39, "million": 0.48, "billion": 0.51, "trillion": 0.51, "quadrillion": 0.52, "quintillion": 0.49 } } ], "total_test_cases": 35, "total_significant": 1 }, "status": "success", "elapsed_s": 0.0, "timestamp": 1783120475.0830643 } ], "edges": [ { "from": "primes_small_s5", "to": "summary", "type": "feeds_summary" }, { "from": "primes_small_s6", "to": "summary", "type": "feeds_summary" }, { "from": "primes_small_s7", "to": "summary", "type": "feeds_summary" }, { "from": "primes_small_s8", "to": "summary", "type": "feeds_summary" }, { "from": "primes_small_s10", "to": "summary", "type": "feeds_summary" }, { "from": "primes_kilo_s5", "to": "summary", "type": "feeds_summary" }, { "from": "primes_kilo_s6", "to": "summary", "type": "feeds_summary" }, { "from": "primes_kilo_s7", "to": "summary", "type": "feeds_summary" }, { "from": "primes_kilo_s8", "to": "summary", "type": "feeds_summary" }, { "from": "primes_kilo_s10", "to": "summary", "type": "feeds_summary" }, { "from": "primes_million_s5", "to": "summary", "type": "feeds_summary" }, { "from": "primes_million_s6", "to": "summary", "type": "feeds_summary" }, { "from": "primes_million_s7", "to": "summary", "type": "feeds_summary" }, { "from": "primes_million_s8", "to": "summary", "type": "feeds_summary" }, { "from": "primes_million_s10", "to": "summary", "type": "feeds_summary" }, { "from": "primes_billion_s5", "to": "summary", "type": "feeds_summary" }, { "from": "primes_billion_s6", "to": "summary", "type": "feeds_summary" }, { "from": "primes_billion_s7", "to": "summary", "type": "feeds_summary" }, { "from": "primes_billion_s8", "to": "summary", "type": "feeds_summary" }, { "from": "primes_billion_s10", "to": "summary", "type": "feeds_summary" }, { "from": "primes_trillion_s5", "to": "summary", "type": "feeds_summary" }, { "from": "primes_trillion_s6", "to": "summary", "type": "feeds_summary" }, { "from": "primes_trillion_s7", "to": "summary", "type": "feeds_summary" }, { "from": "primes_trillion_s8", "to": "summary", "type": "feeds_summary" }, { "from": "primes_trillion_s10", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quadrillion_s5", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quadrillion_s6", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quadrillion_s7", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quadrillion_s8", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quadrillion_s10", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quintillion_s5", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quintillion_s6", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quintillion_s7", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quintillion_s8", "to": "summary", "type": "feeds_summary" }, { "from": "primes_quintillion_s10", "to": "summary", "type": "feeds_summary" } ] }