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 2012-04-10, 22:00 #100 YuL     Feb 2012 Paris, France 7×23 Posts (2^13191*113-1)/903 is prime, N-1 proof, done. (2^13257*71-1)/36351 is prime, N-1 proof, done. (2^13261*3-1)/5 is prime, N-1 proof, done. (2^13285*33-1)/65 is prime, N-1 proof, done. (2^13331*27-1)/215 is prime, N-1 proof, done. (2^13503*159-1)/1271 is prime, N-1 proof, done. (easy thanks to henryzz's prp_provable.txt above)
 2012-04-13, 08:00 #101 YuL     Feb 2012 Paris, France 7·23 Posts (2^10125*25-1)/799, N-1 proof, done. (2^10326*47-1)/3007, N-1 proof, done. (2^10334*37-1)/147, N-1 proof, done. (2^10421*53-1)/1695, N-1 proof, done. (2^10663*23-1)/2943, N-1 proof, done. (2^10712*97-1)/387, N-1 proof, done. (2^10874*7-1)/27, N-1 proof, done. 2^11647-127, N-1 proof, done. (2^14258*17-1)/67, N-1 proof, done. (2^14942*23-1)/91, N-1 proof, done. (2^15916*67-1)/1071, N-1 proof, done. (2^18879*5-1)/39, N-1 proof, done. (thanks to henryzz's prp_provable.txt). Uploading the certificate for ((10^3741*245+43)/9+1)/36 allowed an N+1 proof of (10^3741*245+43)/9.
 2012-04-17, 13:53 #102 wblipp     "William" May 2003 New Haven 22·593 Posts Browsing the smallest PRPs, I found 2^1502*12-5, easily helped to a N-1 proof.
 2012-05-02, 18:50 #103 wblipp     "William" May 2003 New Haven 1001010001002 Posts Here's something new, at least in this thread! This number is (p^3-1)/(13*(p-1)). N-1 has factors of (p-3) and (p+4). This works when the other factors of the cyclotomic (the 13 in this case) can be expressed as k*(k+1)+1. The factors of N-1 are (p-k) and (p+k+1). In loading some OddPerfect factorizations, I've also seen cases with k=1, 2, 4, 9, 28, 60, 68 and 353 although most of those did not produce enough primes to finish the N-1 proof. This one worked with k=3, too. This one worked with k=2
 2012-05-03, 14:01 #104 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 32·79 Posts Can you please tell me the value of p?
 2012-05-03, 18:21 #105 wblipp     "William" May 2003 New Haven 1001010001002 Posts New cases k=7 for this p k=2 for this p The first case above is this p Added in edit: k=4 for this p Last fiddled with by wblipp on 2012-05-04 at 02:10
2012-05-06, 21:27   #106
lorgix

Sep 2010
Scandinavia

3×5×41 Posts

Here are a bunch of 3-PRPs of the form (p^q-1)/(p-1).

Some have proof in the db, some have been proven by Andy Steward et al. and many have never been proven.
Attached Files
 prp.txt (14.1 KB, 190 views)

 2012-05-06, 22:38 #107 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 26AF16 Posts For the low-hanging fruit, the Konyagin-Pomerance can be easily run on more of them -- those that have 30-33.33% factored N+-1. It is a simple script (unlike CHG); easily automated.
 2012-05-19, 08:56 #108 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3·3,301 Posts Phi(1361,717) DB says: "This number is already in queue for N+1-test." :surprised N-1 perhaps?
 2012-06-12, 07:20 #109 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3·3,301 Posts Three Four free gifts for anyone (PRPs are by D.Broadhurst; just prove the N+1 10^3333+y cofactors with threaded Primo; they ECMd easily): 10^9999+658628^3-1 10^9999+1301728^3-1 10^9999+2877590^3-1 10^9999+1570022^3-1 PRP cofactors: Code: (10^3333+1301728)/2^5/5311159/44622313/375265619 has 3309 digits (10^3333+2877590)/4290 has 3330 digits (10^3333+658628)/2/2/3501/32612383/1523444177 has 3313 digits (10^3333+1570022)/2/133461/134268923417549 has 3314 digits Ah, the spirit of sharing... :-) There's one more, I'll do it myself: 10^9999+2779222^3-1
 2013-03-06, 22:48 #110 wblipp     "William" May 2003 New Haven 22×593 Posts Skimming through the list of PRPs, I found this one with an easy P+1 proof (2^6685*9+1)/17

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