類似多胞胎

我們在前一些章節已講解過多重素數組的一些性質和例子,其實我們把多重素數組的 s 值擴大一點,便可找出更多組和多重素數組類同的素數組合,其實這些亦是素數分佈中比較密集的區域。

下列為一些較大的例子:

n=15 / s=58

608181837360884047265507509 + 0, 4, 10, 12, 18, 24, 28, 30, 34, 40, 42, 48, 52, 54, 58
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154241105508041368753 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58
47710850533373130109 + 0, 4, 10, 12, 18, 24, 28, 30, 34, 40, 42, 48, 52, 54, 58

n=15/ s=60


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51376068524333215109383 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 46, 48, 54, 58, 60
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6184360100841504258613 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 48, 54, 58, 60
6040574687609400585583 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 46, 48, 54, 58, 60
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1350075604148915797157 + 0, 2, 6, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60
931358464275011279443 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 60
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728583892785628666723 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 40, 46, 48, 54, 58, 60
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20136435997904751643 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 60
11319107721272355839 + 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50, 60
1325640598359704563 + 0, 4, 6, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60

n=16 / s=62

83019482945581153328297 + 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62
72602373114009889213061 + 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62
2088253704394088213981 + 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62

n=16/ s=66

964013473328959309238981 + 0, 6, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66
126345152364677874751121 + 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 62, 66
90818938277167037444447 + 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 56, 62, 66
90818938277167037444443 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 60, 66
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1914336101631695178377 + 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 62, 66
1379046362703435973487 + 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 50, 54, 56, 62, 66
1379046362703435973483 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 54, 58, 60, 66
1063856088938554404487 + 0, 4, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66
728583892785628666723 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 40, 46, 48, 54, 58, 60, 66
690677476301066467211 + 0, 6, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66
637074904902473997977 + 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 54, 56, 62, 66
333475776718338274037 + 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 50, 54, 56, 62, 66
269337329665351844837 + 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 66
165778774325969932067 + 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 44, 50, 54, 56, 62, 66

n=17 / s=70


90818938277167037444443 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 60, 66, 70
12025162080993908389537 + 0, 4, 10, 12, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
9328108048727233598827 + 0, 4, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
1379046362703435973483 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 54, 58, 60, 66, 70

n=17 / s=72

34840334124833280031 + 0, 6, 10, 16, 18, 22, 28, 30, 36, 46, 48, 52, 58, 60, 66, 70, 72

n=17 / s=76

55166172881845055253211 + 0, 6, 10, 18, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76
19472663925881531488111 + 0, 10, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76
11490035915853116358673 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 46, 54, 58, 60, 66, 70, 76
3525391639439773250083 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 46, 48, 54, 58, 60, 66, 70, 76
728583892785628666723 + 0, 4, 6, 10, 16, 18, 24, 28, 30, 40, 46, 48, 54, 58, 60, 66, 76

n=18 / s=82

53947453971035573715691 + 0, 16, 18, 22, 28, 30, 36, 40, 42, 46, 52, 58, 60, 66, 70, 72, 78, 82

n=18 / s=84

121588305945933223037 + 0, 2, 6, 12, 14, 20, 26, 32, 36, 42, 44, 50, 54, 56, 60, 62, 72, 84
105151328771084515817 + 0, 2, 24, 30, 32, 36, 42, 44, 50, 56, 60, 62, 66, 72, 74, 80, 84, 86

 

參考文獻及網址:

Forbes, T. "Prime k-Tuplets." http://www.ltkz.demon.co.uk/ktuplets.htm.

 

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