Share N+/-1 Primality Proofs

[YuL]

(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)

[YuL]

(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.

[wblipp]

Browsing the smallest PRPs, I found 2^1502*12-5, easily helped to a N-1 proof.

[wblipp]

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

[Stargate38]

Can you please tell me the value of p?

[wblipp]

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

[lorgix]

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.

[Batalov]

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.

[Batalov]

Phi(1361,717)

DB says: "This number is already in queue for N+1-test." :surprised
N-1 perhaps?

[Batalov]

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:

(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

[wblipp]

Skimming through the list of PRPs, I found this one with an easy P+1 proof

(2^6685*9+1)/17