2^F4-1

davar55 · 2008-05-14, 21:49

I'm just wondering: since Mersenne included 2^257-1 in his list
of primes, and it is composite and completely factored,
what is the factorization status of 2^65537-1? The factoring
applet I tried doesn't try numbers that large. Have any small
factors been found? (I realize it must be composite.)

philmoore · 2008-05-14, 22:55

Yes indeed, although M65537 was proven composite by a Lucas-Lehmer test many years ago, it is only recently that two small factors have been found. See this thread:
http://www.mersenneforum.org/showthread.php?t=8130
The smaller factor was apparently found in early November 2006 but had been missed earlier by a probably buggy version of Prime95. The cofactor is composite.

Andi47 · 2008-05-20, 15:40

P-1 with B1 = 1e6, B2 = 1e9: no factor found.

2008-05-14, 21:49	#1
davar55 May 2004 New York City 10213₈ Posts	2^F4-1 I'm just wondering: since Mersenne included 2^257-1 in his list of primes, and it is composite and completely factored, what is the factorization status of 2^65537-1? The factoring applet I tried doesn't try numbers that large. Have any small factors been found? (I realize it must be composite.)

2008-05-14, 22:55	#2
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 10001011111₂ Posts	Yes indeed, although M65537 was proven composite by a Lucas-Lehmer test many years ago, it is only recently that two small factors have been found. See this thread: http://www.mersenneforum.org/showthread.php?t=8130 The smaller factor was apparently found in early November 2006 but had been missed earlier by a probably buggy version of Prime95. The cofactor is composite. Last fiddled with by philmoore on 2008-05-14 at 22:55

2008-05-20, 15:40	#3
Andi47 Oct 2004 Austria 4662₈ Posts	P-1 with B1 = 1e6, B2 = 1e9: no factor found.