mersenneforum.org Searching for generalized repunit PRP
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2016-12-06, 14:52   #1
sweety439

Nov 2016

236310 Posts
Searching for generalized repunit PRP

Is there a project to search the (probable) primes of the form (b^n-1)/(b-1) (generalized repunit base b) or (b^n+1)/(b+1) (generalized repunit base -b)? There are links to this, http://www.fermatquotient.com/PrimSerien/GenRepu.txt (base b for 2<=b<=152)

http://www.fermatquotient.com/PrimSerien/GenRepuP.txt (base -b for 2<=b<=152)

These are text files I searched the repunit PRP for b up to +-257 and n up to 10000.
Attached Files
 repunit base 2 to 257.txt (6.2 KB, 137 views) repunit base -2 to -257.txt (6.3 KB, 152 views)

 2016-12-06, 14:58 #2 sweety439     Nov 2016 93B16 Posts Some bases have algebra factors. These bases are numbers of the form k^r with integer k != 1, 0, -1 and integer r > 1, and numbers of the form -4k^4 with integer k > 0. The list of all such bases are ..., -1024, -1000, -729, -512, -343, -243, -216, -125, -64, -32, -27, -8, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 144, 169, 196, 216, 225, 243, 256, 289, 324, 343, 361, 400, 441, 484, 512, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1000, 1024, ... and ..., -5184, -2500, -1024, -324, -64, -4.
 2016-12-06, 15:03 #3 sweety439     Nov 2016 17×139 Posts Also, the link is the searching for primes of the form (a+1)^n-a^n: http://www.fermatquotient.com/PrimSerien/PrimPot.txt. More generally, is there a project to search for primes of the forms (a^n-b^n)/(a-b) with a>1, -a
 2016-12-06, 15:38 #4 paulunderwood     Sep 2002 Database er0rr 2×1,723 Posts Some are cofactors... (a^p-1)/n (a^p+1)/n (a^p-b^p)/n (a^p+b^p)/n
 2016-12-07, 01:35 #5 carpetpool     "Sam" Nov 2016 31610 Posts I don't think there is a project (just yet) but I am starting my own (I don't know if you'd find it interesting or not) for find PRP factors of numbers of the form (b^n-1)/(b-1) or (a+1)^n-a^n. As far as I know for both projects, All prime bases b < 10000 (for (b^n-1)/(b-1)) are tested to 20k digits. PRP factors found and tested. FYI All bases a < 100 (for (a+1)^n-a^n) are tested to 20k digits. PRP factors found and tested. Hope this helps. Check out here. Last fiddled with by carpetpool on 2016-12-07 at 02:08
 2016-12-07, 11:26 #6 sweety439     Nov 2016 1001001110112 Posts Before, I used factordb.com to find all repunit PRPs with 152<=b<=257 and -257<=b<=-152 and n<=10000. Since in http://www.fermatquotient.com/, it was already searched for 2<=b<=151 and -151<=b<=-2.
2016-12-07, 11:35   #7
sweety439

Nov 2016

236310 Posts

These are files that I found the smallest odd prime p such that (b^p-1)/(b-1) or (b^p+1)/(b+1) is (probable) prime for 2<=b<=1025, and the smallest prime p such that (b+1)^p-b^p is (probable) prime for 1<=b<=1024. (not all (probable) primes are founded by me)
Attached Files
 least odd prime p such that (n^p-1)(n-1) is prime.txt (8.7 KB, 164 views) least odd prime p such that (n^p+1)(n+1) is prime.txt (8.1 KB, 86 views) least prime p such that (n+1)^p-n^p is prime.txt (9.9 KB, 100 views)

2016-12-07, 11:46   #8
sweety439

Nov 2016

17·139 Posts

Also, I have searched the smallest odd prime p such that (a^p-b^p)/(a-b) is prime for 1<a<=50, -a<b<a, and a and b are coprime. (for (a^p+b^p)/(a+b), note that since p is odd, it equals (a^p-(-b)^p)/(a-(-b)))

All of the "NA" terms were searched to at least p=10000. (0 if no possible prime)
Attached Files
 least odd prime p such that (a^p-b^p)(a-b) is prime.txt (17.5 KB, 99 views)

Last fiddled with by sweety439 on 2016-12-07 at 11:48

 2016-12-07, 16:03 #9 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23A816 Posts 'Those who don't know history are doomed to repeat it.' (George Santayana) Would you please stop reposting in every possible forum thread trivial results that are known for a century? Sadly you forgot to post in http://mersenneforum.org/forumdisplay.php?f=24 that for 1
 2016-12-07, 18:12 #10 sweety439     Nov 2016 17·139 Posts No, it is (a^p-b^p)/(a-b), not 2^a-1. This a is the base, not the exponent. The file in that post lists the smallest odd prime p such that (a^p-b^p)/(a-b) is prime. (for 1
 2016-12-10, 00:46 #11 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23×7×163 Posts (49^16747+46^16747)/95 is a PRP ... Too small for PRPtop - the limit was raised to 30000 digits. (46^45281+11^45281)/57 is a PRP Btw, I wonder if you know how to sieve them properly. Or is it "up to the first 10000 primes"? (Hint: most of the small primes will not divide any of these candidates.) Last fiddled with by Batalov on 2016-12-10 at 22:40

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