Needed: gaps between large primes
Pfoertner, Hugo
Hugo.Pfoertner at muc.mtu.de
Mon Nov 3 14:33:49 CET 2003
Dear Marian,
you asked Neil Sloane for examples of gaps between large prime numbers to
test
programs developed by yourself and your students.
It's extremely easy to create such numbers using OpenPFGW
which was available at http://www.primeform.net/openpfgw/ ,
but this address currently? seems to be offline.
OpenPFGW can handle numbers of several 10000 digits.
Here are the first entries: (differences computed with Excel)
Primes Gap
39+ 10^20 129 90
129+ 10^20 151 22
151+ 10^20 193 42
193+ 10^20 207 14
207+ 10^20 301 94
301+ 10^20 349 48
349+ 10^20 361 12
361+ 10^20 391 30
391+ 10^20 393 2
393+ 10^20 441 48
441+ 10^20 477 36
477+ 10^20 547 70
547+ 10^20 559 12
559+ 10^20 561 2
561+ 10^20 721 160
721+ 10^20 741 20
741+ 10^20 753 12
753+ 10^20 757 4
757+ 10^20 763 6
763+ 10^20 801 38
801+ 10^20 853 52
853+ 10^20 961 108
961+ 10^20 993 32
993+ 10^20 1071 78
1071+ 10^20 1107 36
1107+ 10^20 1119 12
1119+ 10^20 1141 22
1141+ 10^20 1197 56
1197+ 10^20 1221 24
1221+ 10^20 1243 22
1243+ 10^20 1261 18
1261+ 10^20 1267 6
1267+ 10^20 1303 36
1303+ 10^20 1323 20
1323+ 10^20 1387 64
1387+ 10^20 1521 134
1521+ 10^20 1537 16
1537+ 10^20 1567 30
1567+ 10^20 1597 30
1597+ 10^20 1633 36
1633+ 10^20 1663 30
1663+ 10^20 1677 14
1677+ 10^20 1821 144
1821+ 10^20 1827 6
1827+ 10^20 1893 66
1893+ 10^20 1921 28
1921+ 10^20 1977 56
1977+ 10^20 1983 6
1983+ 10^20 2013 30
2013+ 10^20 2073 60
2073+ 10^20 2187 114
2187+ 10^20 2277 90
2277+ 10^20 2317 40
2317+ 10^20 2349 32
2349+ 10^20 2479 130
2479+ 10^20 2493 14
2493+ 10^20 2559 66
2559+ 10^20 2607 48
2607+ 10^20 2659 52
2659+ 10^20 2667 8
2667+ 10^20 2691 24
2691+ 10^20 2697 6
2697+ 10^20 2817 120
2817+ 10^20 2829 12
2829+ 10^20 2871 42
2871+ 10^20 2913 42
2913+ 10^20 2967 54
2967+ 10^20 2983 16
2983+ 10^20 3003 20
3003+ 10^20 3051 48
3051+ 10^20 3087 36
3087+ 10^20 3097 10
3097+ 10^20 3103 6
3103+ 10^20 3121 18
3121+ 10^20 3129 8
3129+ 10^20 3247 118
3247+ 10^20 3307 60
3307+ 10^20 3313 6
3313+ 10^20 3327 14
3327+ 10^20 3363 36
3363+ 10^20 3367 4
3367+ 10^20 3381 14
3381+ 10^20 3429 48
3429+ 10^20 3457 28
3457+ 10^20 3483 26
3483+ 10^20 3499 16
3499+ 10^20 3577 78
3577+ 10^20 3847 270
3847+ 10^20 3867 20
3867+ 10^20 3903 36
3903+ 10^20 3931 28
3931+ 10^20 3961 30
3961+ 10^20 4143 182
4143+ 10^20 4159 16
4159+ 10^20 4237 78
4237+ 10^20 4239 2
4239+ 10^20 4249 10
4249+ 10^20 4291 42
4291+ 10^20 4329 38
4329+ 10^20 4357 28
4357+ 10^20 4477 120
4477+ 10^20 4491 14
4491+ 10^20 4503 12
4503+ 10^20 4519 16
4519+ 10^20 4533 14
4533+ 10^20 4539 6
4539+ 10^20 4617 78
4617+ 10^20 4647 30
4647+ 10^20 4731 84
4731+ 10^20 4843 112
4843+ 10^20 4857 14
4857+ 10^20 4893 36
4893+ 10^20 4953 60
4953+ 10^20 4987 34
4987+ 10^20 5053 66
If you need more just write, but I recommend to get one
of the available programs and to consult the Prime Pages:
http://www.utm.edu/research/primes/ giving a lot of
information and links.
Best regards
Hugo Pfoertner
-----Ursprüngliche Nachricht-----
Von: N. J. A. Sloane [mailto:njas at research.att.com]
Gesendet am: 03 November, 2003 13:40
An: seqfan at ext.jussieu.fr
Cc: njas at research.att.com
Betreff: Needed: gaps between large primes
Dear SeqFans, I got the following message from someone
in Poland - a teacher who needs help. He (I think from
the word endings the author is a man) would like
a list of gaps between successive primes for primes
with 20 digits or more.
Can someone help him? Let M = 10^20. Can someone produce
the sequence
prime(k+1)-prime(k) , k=M..M+100 (say),
and send it to him? If you can help please post a message here to
avoid duplication of effort - and please send me a copy.
Thanks
Neil Sloane
[...]
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