Leave it to the computers - will you? - Page 2

bsquared · 2013-03-22, 16:47

Quote:

Originally Posted by xilman

Surely that's how anyone would factor something that small and that well known these days? Perhaps you may not have the luxury of a local file but it wouldn't take either factordb or Google much longer.

It would have taken me longer to look up online than it did to type it into an already open csh.

For the record, I was looking it up in parallel... but yafu beat me to the results.

Dubslow · 2013-03-22, 17:03

Quote:

Originally Posted by bsquared

It would have taken me longer to look up online than it did to type it into an already open csh.

csh?

That's the first time i've actually heard of anyone using it.

Quote:

For the record, I was looking it up in parallel... but yafu beat me to the results.

You of all people certainly know it's good stuff.

Mr. P-1 · 2013-03-22, 18:55

Quote:

Originally Posted by Dubslow

csh?

That's the first time i've actually heard of anyone using it.

I remember using it when I was at uni in the early 80s.

henryzz · 2013-03-22, 19:04

Apart from the poor implementation issues(which surely could now be corrected?) it looks quite useful. The syntax doesn't look as criptic as perl at first glance.

storflyt32 · 2013-04-03, 16:30

If you check out http://en.wikipedia.org/wiki/Mersenne_prime, it is known from this list that there are a total of 48 known Mersenne primes on the form 2^n-1.

The largest one being the recent discovery of 2^57,885,161-1 .

But when adding 1 to 2^n, apparently 65537 is still the largest known Fermat prime. The list at http://en.wikipedia.org/wiki/Fermat_prime gives the factors for F0 through F11.

My question is then as follows. If using a LLR algorithm or a Genefer specific equivalent to this, how far or high up has this been tested right now when it comes to the possible primality of numbers when it comes to adding 1 when compared to the similar subtraction of 1?

Meaning - testing out whether 2^n + 1 is a prime (n being a very big number, possibly similar to n=57,885,161 mentioned above).

jasonp · 2013-04-03, 16:39

For 2^n+1 it's easy to prove that only Fermat numbers (with n=2^k for some k) have a chance of being prime. These numbers grow very quickly in size; the first such number that might be prime is n=2^33, and short of trial division (which a lot of people have done) there's just no telling. Look up the Pepin test for a deterministic primality test for Fermat numbers. Definitely do not try it on F33 though.

2013-04-03, 16:30	#16
storflyt32 Feb 2013 2×229 Posts	Which number could be prime for 2^n+1? If you check out http://en.wikipedia.org/wiki/Mersenne_prime, it is known from this list that there are a total of 48 known Mersenne primes on the form 2^n-1. The largest one being the recent discovery of 2^57,885,161-1 . But when adding 1 to 2^n, apparently 65537 is still the largest known Fermat prime. The list at http://en.wikipedia.org/wiki/Fermat_prime gives the factors for F0 through F11. My question is then as follows. If using a LLR algorithm or a Genefer specific equivalent to this, how far or high up has this been tested right now when it comes to the possible primality of numbers when it comes to adding 1 when compared to the similar subtraction of 1? Meaning - testing out whether 2^n + 1 is a prime (n being a very big number, possibly similar to n=57,885,161 mentioned above).

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2013-03-22, 19:04	#15
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 2³·3·5·7² Posts	Apart from the poor implementation issues(which surely could now be corrected?) it looks quite useful. The syntax doesn't look as criptic as perl at first glance.

2013-04-03, 16:39	#17
jasonp Tribal Bullet Oct 2004 DD5₁₆ Posts	For 2^n+1 it's easy to prove that only Fermat numbers (with n=2^k for some k) have a chance of being prime. These numbers grow very quickly in size; the first such number that might be prime is n=2^33, and short of trial division (which a lot of people have done) there's just no telling. Look up the Pepin test for a deterministic primality test for Fermat numbers. Definitely do not try it on F33 though.