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2019-06-04, 14:14   #56
sweety439

Nov 2016

22·691 Posts

Kar_bon, there are many known primes of the form (b+-1)*b^n+-1 and b^n+-(b+-1) for b<=16 that are not currently in the corresponding OEIS sequence, thus you can extend these OEIS sequences:

Quote:
 For the n such that these forms is prime: a1(b): numbers n such that (b-1)*b^n-1 is prime a2(b): numbers n such that (b-1)*b^n+1 is prime a3(b): numbers n such that (b+1)*b^n-1 is prime a4(b): numbers n such that (b+1)*b^n+1 is prime (not exist when b == 1 mod 3) a5(b): numbers n such that b^n-(b-1) is prime a6(b): numbers n such that b^n+(b-1) is prime a7(b): numbers n such that b^n-(b+1) is prime a8(b): numbers n such that b^n+(b+1) is prime (not exist when b == 1 mod 3) Using "------------" if there is currently no OEIS sequence, "xxxxxxx" if such n not exist (only for a4(b) and a8(b) for b == 1 mod 3) b a1(b) a2(b) a3(b) a4(b) a5(b) a6(b) a7(b) a8(b) 2 A000043 ------------ A002235 A002253 A000043 ------------ A050414 A057732 3 A003307 A003306 A005540 A005537 A014224 A051783 A058959 A058958 4 A272057 ------------ ------------ xxxxxxx A059266 A089437 A217348 xxxxxxx 5 A046865 A204322 A257790 A143279 A059613 A124621 A165701 A089142 6 A079906 A247260 ------------ ------------ A059614 A145106 A217352 A217351 7 A046866 A245241 ------------ xxxxxxx A191469 A217130 A217131 xxxxxxx 8 A268061 A269544 ------------ ------------ A217380 A217381 A217383 A217382 9 A268356 A056799 ------------ ------------ A177093 A217385 A217493 A217492 10 A056725 A056797 A111391 xxxxxxx A095714 A088275 A092767 xxxxxxx 11 A046867 A057462 ------------ ------------ ------------ ------------ ------------ ------------ 12 A079907 A251259 ------------ ------------ ------------ A137654 ------------ ------------ 13 A297348 ------------ ------------ xxxxxxx ------------ ------------ ------------ xxxxxxx 14 A273523 ------------ ------------ ------------ ------------ ------------ ------------ ------------ 15 ------------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ 16 ------------ ------------ ------------ xxxxxxx ------------ ------------ ----------- xxxxxxx
e.g. A217352: a7(6), 6^n-(6+1) is prime for n=2, 4, 6, 8, 9, 10, 15, 20, 46, 49, 61, 98, 110, 144, 266, 344, 978, 1692, 1880, 1924, 3142, 3220, 4209, 5708, 7064, 13465, 13858, 19474, 22666, but currently the sequence only lists the terms up to 7064.

Also, you can extended the sequence A122396 (exactly the Williams primes MM with prime b) up to n=50 and A087139 (exactly the Williams MP with prime b) up to n=91. (e.g. A087139(54) = 102979, since (251-1)*251^102978+1 is prime, and this number equals 251^102979 - 251^102978 + 1)

Last fiddled with by kar_bon on 2019-06-06 at 08:35 Reason: table

 2019-06-04, 21:26 #57 matzetoni     Feb 2019 34 Posts https://www.rieselprime.de/ziki/Williams_prime_PP_3 Just wanted to let you know that I'm still searching on the numbers above. I already finished to n=800k without new primes.
2019-06-04, 22:10   #58
kar_bon

Mar 2006
Germany

54628 Posts

Quote:
 Originally Posted by matzetoni https://www.rieselprime.de/ziki/Williams_prime_PP_3 Just wanted to let you know that I'm still searching on the numbers above. I already finished to n=800k without new primes.
Thanks, marked WilliamsPP3 as reserved by you and added a history entry.

 2019-06-05, 08:06 #59 kar_bon     Mar 2006 Germany 1011001100102 Posts @sweety439: Plases do me a favour: Take a range or a dozen bases, test them to n=10k, attach a file with the primes with the range done. I will not update the Wiki every day for your small primes and no searched range given. For example the next prime for MM 126 is less 10000. Last fiddled with by kar_bon on 2019-06-06 at 08:32 Reason: addressed
 2019-06-05, 08:11 #60 kar_bon     Mar 2006 Germany 286610 Posts I've included a separate page for all remaining data for Williams primes (for now only MM-type). Listed are all bases b < 2050 not yet available as own page and n-max=1000 or given range.
 2019-06-06, 07:14 #61 kar_bon     Mar 2006 Germany 54628 Posts @sweety439 I've deleted your posts with results here! This is the thread for the Wiki not for your results. Please post those in your own threads.
 2019-06-09, 00:02 #62 sweety439   Nov 2016 22×691 Posts In the page Proth prime small bases least n, the data is not correct: the forms 2*512^n+1, 4*32^n+1, 4*512^n+1, 4*1024^n+1, 10*1000^n+1 and 12*12^n+1 may have primes, since it is not known whether there are Fermat primes > 2^(2^4)+1, etc. (all these numbers are generalized Fermat numbers). (Note that such forms do not include 8*128^n+1, 8*128^n+1 have no possible primes) Also, recently a prime 7*1004^54848+1 was found, please add it.
 2019-06-09, 00:10 #63 sweety439   Nov 2016 ACC16 Posts There are other sequences for Riesel/Proth prime small bases least n: (not only A119591 and A253178) A119624 (Proth k=2, 0 for bases with no possible prime) A088782 (Proth k=10, 0 for bases with no possible prime) A098873 (Riesel k=2 for bases divisible by 6) A098872 (Proth k=2 for bases divisible by 6) A098876 (Riesel k=3 for bases divisible by 6) A098877 (Proth k=3 for bases divisible by 6) Last fiddled with by sweety439 on 2019-06-09 at 00:11
 2019-06-10, 14:39 #64 WGJC3107     "Will Conway" May 2018 UK 26 Posts Is it possible for you to add Operation Billion Digits as a project on the wiki?I can’t seem to find any mention of it. Last fiddled with by WGJC3107 on 2019-06-10 at 14:39
2019-06-10, 14:42   #65
Dylan14

"Dylan"
Mar 2017

54710 Posts

Quote:
 Originally Posted by WGJC3107 Is it possible for you to add Operation Billion Digits as a project on the wiki?I can’t seem to find any mention of it.
It is in the wiki, see here.

 2019-06-10, 15:25 #66 WGJC3107     "Will Conway" May 2018 UK 26 Posts Thanks, I didn’t realise there was a page there. Is it possible for me to make an account on there to edit pages or is that just admin’s job?

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