[QUOTE=chris2be8;401756]I'll have to try that next time I find an interesting PRP. About how long would it take for a number this size and how many bases do I need to try to be reasonably sure it's prime?

Chris[/QUOTE]

About 2-3 seconds (or more, but in that ballpark). Base 2 derived numbers (factors of 2^n+/-1) will pass base-2 test regardless of whether they are prime or composite. Similarly base-3 derived numbers will pass base-3 test (etc.). Personally, I try 3,5,7,11. For larger numbers, I check _fewer_ bases.

(296^1303+1)/297 ([url]http://www.factordb.com/index.php?id=1100000000667022093[/url]) is very close to being provable. N-1 has received 2 t25 and N+1 has received 2 t20. Anyone care to try their luck with further ECM? (FYI, at 3200 digits, it is probably cheaper to just prove it by ECPP, but there is something satisfying about getting an N-1 proof)

K-P proof is a very easy proof: much easier than additional ECM.
It is fun to implement from scratch... or one can use an old script in primeform yahoo group files.

[QUOTE=Batalov;401826]K-P proof is a very easy proof: much easier than additional ECM.
It is fun to implement from scratch... or one can use an old script in primeform yahoo group files.[/QUOTE]

Does factordb accept those?

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Proving a PRP1010 ([url]http://www.factordb.com/index.php?id=1100000000777552536[/url]) will allow the N-1 proof of (3282^919-1)/3281 ([url]http://www.factordb.com/index.php?id=1100000000599224872[/url]). Incidentally, during the ECM, another PRP326 also popped out ([url]http://www.factordb.com/index.php?id=1100000000777552532[/url]), but proving that wouldn't have been sufficient. Actually, just the 2 PRPs are sufficient in themselves.

Primitive part of 2,21542L (I hope my notation is correct). (2^21542+1)/(2^10771+2^5386+1)/5 ([url]http://www.factordb.com/index.php?id=1100000000007178552[/url]). Proved by N-1

Proving a PRP851 ([url]http://www.factordb.com/index.php?id=1100000000777573161[/url]) will complete the N-1 proof of 9^3406-8 ([url]http://www.factordb.com/index.php?id=1100000000294959334[/url])

[QUOTE=axn;401833]Primitive part of 2,21542L (I hope my notation is correct). (2^21542+1)/(2^10771+2^5386+1)/5 [/QUOTE]
It is indeed, and it is an "Eisenstein-Mersenne cofactor". (not a Generalized Unique prime, though)
Can be written as Phi(4,2^5386-1)/10, whereas Eisenstein-Mersenne primes are Phi(4,2^n+-1)/2.

[QUOTE=axn;401824](296^1303+1)/297 ([url]http://www.factordb.com/index.php?id=1100000000667022093[/url]) is very close to being provable. N-1 has received 2 t25 and N+1 has received 2 t20. Anyone care to try their luck with further ECM? (FYI, at 3200 digits, it is probably cheaper to just prove it by ECPP, but there is something satisfying about getting an N-1 proof)[/QUOTE]

After a few hundred curves at t35, a P36 popped out, allowing the completion of N-1 proof.

[QUOTE=lorgix;401768] Define reasonably. [/QUOTE]

Less than 1/100 chance it's not a prime would be a reasonable probability to ask for help proving it prime.

Chris

[QUOTE=axn;401813]Base 2 derived numbers (factors of 2^n+/-1) will pass base-2 test regardless of whether they are prime or composite. [/QUOTE]

Does that mean that finding a base 2 derived number that's a Lucas pseudoprime would find a BPSW pseudoprime? Or is there no chance of finding one?

Chris

Proving [url]http://factordb.com/index.php?id=1100000000777707215[/url] (1035 digits) and [url]http://factordb.com/index.php?id=1100000000777707223[/url] (687 digits) should enable a N+1 proof that [url]http://factordb.com/index.php?id=1100000000213107758[/url], 2^66878-2^1358-1, (20133 digits) is prime. I've checked both PRPs with bases 3, 5, 7, 11 and 13 so they should not turn out to be composites this time.

Chris