回复：N连续合数之和(N≥3)中的素数有限性猜想

区间 [100000000000000000000000000000000004200000, 100000000000000000000000000000000004250000] k=5 连 续合数统计 =====
合数总数：49448
5连续合数总组数：49444
和为素数组数：2
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0039
和为素数条目清单：
1. (100000000000000000000000000000000004235974, 100000000000000000000000000000000004235975, 100000000000000000000000000000000004235976, 100000000000000000000000000000000004235978, 100000000000000000000000000000000004235980) , S=500000000000000000000000000000000021179883 ✔
2. (100000000000000000000000000000000004235976, 100000000000000000000000000000000004235978, 100000000000000000000000000000000004235980, 100000000000000000000000000000000004235981, 100000000000000000000000000000000004235982) , S=500000000000000000000000000000000021179897 ✔

区间 [100000000000000000000000000000000004300000, 100000000000000000000000000000000004350000] k=5 连 续合数统计 =====
合数总数：49480
5连续合数总组数：49476
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000004343580, 100000000000000000000000000000000004343582, 100000000000000000000000000000000004343584, 100000000000000000000000000000000004343585, 100000000000000000000000000000000004343586) , S=500000000000000000000000000000000021717917 ✔

区间 [100000000000000000000000000000000004350000, 100000000000000000000000000000000004400000] k=5 连 续合数统计 =====
合数总数：49465
5连续合数总组数：49461
和为素数组数：2
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0039
和为素数条目清单：
1. (100000000000000000000000000000000004353660, 100000000000000000000000000000000004353662, 100000000000000000000000000000000004353664, 100000000000000000000000000000000004353665, 100000000000000000000000000000000004353666) , S=500000000000000000000000000000000021768317 ✔
2. (100000000000000000000000000000000004368388, 100000000000000000000000000000000004368389, 100000000000000000000000000000000004368390, 100000000000000000000000000000000004368392, 100000000000000000000000000000000004368394) , S=500000000000000000000000000000000021841953 ✔

区间 [100000000000000000000000000000000004550000, 100000000000000000000000000000000004600000] k=5 连 续合数统计 =====
合数总数：49497
5连续合数总组数：49493
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000004591680, 100000000000000000000000000000000004591682, 100000000000000000000000000000000004591684, 100000000000000000000000000000000004591685, 100000000000000000000000000000000004591686) , S=500000000000000000000000000000000022958417 ✔

区间 [100000000000000000000000000000000004600000, 100000000000000000000000000000000004650000] k=5 连 续合数统计 =====
合数总数：49462
5连续合数总组数：49458
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000004638418, 100000000000000000000000000000000004638419, 100000000000000000000000000000000004638420, 100000000000000000000000000000000004638422, 100000000000000000000000000000000004638424) , S=500000000000000000000000000000000023192103 ✔

区间 [100000000000000000000000000000000005050000, 100000000000000000000000000000000005100000] k=5 连 续合数统计 =====
合数总数：49514
5连续合数总组数：49510
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000005091754, 100000000000000000000000000000000005091755, 100000000000000000000000000000000005091756, 100000000000000000000000000000000005091758, 100000000000000000000000000000000005091760) , S=500000000000000000000000000000000025458783 ✔

区间 [100000000000000000000000000000000005250000, 100000000000000000000000000000000005300000] k=5 连 续合数统计 =====
合数总数：49468
5连续合数总组数：49464
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000005256360, 100000000000000000000000000000000005256362, 100000000000000000000000000000000005256364, 100000000000000000000000000000000005256365, 100000000000000000000000000000000005256366) , S=500000000000000000000000000000000026281817 ✔

所有五连续合数，其和为素数的条目，直径(p₅-p₁)均不超过6吗？
和为素数条目清单：
1. (4, 6, 8, 9, 10) , S=37 ✔
2. (8, 9, 10, 12, 14) , S=53 ✔
3. (10, 12, 14, 15, 16) , S=67 ✔
4. (14, 15, 16, 18, 20) , S=83 ✔
5. (16, 18, 20, 21, 22) , S=97 ✔
6. (28, 30, 32, 33, 34) , S=157 ✔
7. (56, 57, 58, 60, 62) , S=293 ✔
8. (58, 60, 62, 63, 64) , S=307 ✔
9. (68, 69, 70, 72, 74) , S=353 ✔
10. (70, 72, 74, 75, 76) , S=367 ✔
11. (106, 108, 110, 111, 112) , S=547 ✔
12. (134, 135, 136, 138, 140) , S=683 ✔
13. (146, 147, 148, 150, 152) , S=743 ✔…
和为素数条目已知最大：
(10^41+5256360, 10^41+5256362, 10^41+5256364, 10^41+5256365, 10^41+5256366) , S=5*10^41+26281817 ✔

区间 [100000000000000000000000000000000005250000, 100000000000000000000000000000000005300000] k=5 连 续合数统计 =====
合数总数：49468
5连续合数总组数：49464
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000005256360, 100000000000000000000000000000000005256362, 100000000000000000000000000000000005256364, 100000000000000000000000000000000005256365, 100000000000000000000000000000000005256366) , S=500000000000000000000000000000000026281817 ✔

区间 [100000000000000000000000000000000005400000, 100000000000000000000000000000000005450000] k=5 连 续合数统计 =====
合数总数：49455
5连续合数总组数：49451
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000005417778, 100000000000000000000000000000000005417780, 100000000000000000000000000000000005417782, 100000000000000000000000000000000005417783, 100000000000000000000000000000000005417784) , S=500000000000000000000000000000000027088907 ✔

区间 [100000000000000000000000000000000005400000, 100000000000000000000000000000000005450000] k=5 连 续合数统计 =====
合数总数：49455
5连续合数总组数：49451
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000005417778, 100000000000000000000000000000000005417780, 100000000000000000000000000000000005417782, 100000000000000000000000000000000005417783, 100000000000000000000000000000000005417784) , S=500000000000000000000000000000000027088907 ✔

区间 [100000000000000000000000000000000005700000, 100000000000000000000000000000000005750000] k=5 连 续合数统计 =====
合数总数：49477
5连续合数总组数：49473
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000005747430, 100000000000000000000000000000000005747432, 100000000000000000000000000000000005747434, 100000000000000000000000000000000005747435, 100000000000000000000000000000000005747436) , S=500000000000000000000000000000000028737167 ✔

区间 [100000000000000000000000000000000006050000, 100000000000000000000000000000000006100000] k=5 连 续合数统计 =====
合数总数：49474
5连续合数总组数：49470
和为素数组数：2
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0039
和为素数条目清单：
1. (100000000000000000000000000000000006055528, 100000000000000000000000000000000006055529, 100000000000000000000000000000000006055530, 100000000000000000000000000000000006055532, 100000000000000000000000000000000006055534) , S=500000000000000000000000000000000030277653 ✔
2. (100000000000000000000000000000000006055654, 100000000000000000000000000000000006055655, 100000000000000000000000000000000006055656, 100000000000000000000000000000000006055658, 100000000000000000000000000000000006055660) , S=500000000000000000000000000000000030278283 ✔

区间 [100000000000000000000000000000000006150000, 100000000000000000000000000000000006200000] k=5 连 续合数统计 =====
合数总数：49465
5连续合数总组数：49461
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000006158178, 100000000000000000000000000000000006158180, 100000000000000000000000000000000006158182, 100000000000000000000000000000000006158183, 100000000000000000000000000000000006158184) , S=500000000000000000000000000000000030790907 ✔
区间 [100000000000000000000000000000000006200000, 100000000000000000000000000000000006250000] k=5 连 续合数统计 =====
合数总数：49493
5连续合数总组数：49489
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000006239578, 100000000000000000000000000000000006239579, 100000000000000000000000000000000006239580, 100000000000000000000000000000000006239582, 100000000000000000000000000000000006239584) , S=500000000000000000000000000000000031197903 ✔
区间 [100000000000000000000000000000000006400000, 100000000000000000000000000000000006450000] k=5 连 续合数统计 =====
合数总数：49456
5连续合数总组数：49452
和为素数组数：2
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0039
和为素数条目清单：
1. (100000000000000000000000000000000006441810, 100000000000000000000000000000000006441812, 100000000000000000000000000000000006441814, 100000000000000000000000000000000006441815, 100000000000000000000000000000000006441816) , S=500000000000000000000000000000000032209067 ✔
2. (100000000000000000000000000000000006443460, 100000000000000000000000000000000006443462, 100000000000000000000000000000000006443464, 100000000000000000000000000000000006443465, 100000000000000000000000000000000006443466) , S=500000000000000000000000000000000032217317 ✔

区间 [100000000000000000000000000000000006450000, 100000000000000000000000000000000006500000] k=5 连 续合数统计 =====
合数总数：49468
5连续合数总组数：49464
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000006459796, 100000000000000000000000000000000006459797, 100000000000000000000000000000000006459798, 100000000000000000000000000000000006459800, 100000000000000000000000000000000006459802) , S=500000000000000000000000000000000032298993 ✔
区间 [100000000000000000000000000000000006550000, 100000000000000000000000000000000006600000] k=5 连 续合数统计 =====
合数总数：49499
5连续合数总组数：49495
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000006599238, 100000000000000000000000000000000006599240, 100000000000000000000000000000000006599242, 100000000000000000000000000000000006599243, 100000000000000000000000000000000006599244) , S=500000000000000000000000000000000032996207 ✔
区间 [100000000000000000000000000000000008500000, 100000000000000000000000000000000008550000] k=5 连 续合数统计 =====
合数总数：49478
5连续合数总组数：49474
和为素数组数：1
S平均值 S_avg = 500000000000000022442856339037958392774656.0000
α = 0.0000
β = 1/ln(S_avg) = 0.0104
γ = α/β = 0.0019
和为素数条目清单：
1. (100000000000000000000000000000000008510728, 100000000000000000000000000000000008510729, 100000000000000000000000000000000008510730, 100000000000000000000000000000000008510732, 100000000000000000000000000000000008510734) , S=500000000000000000000000000000000042553653 ✔