mersenneforum.org > Math is there only one Mersenne prime that ends in 3?
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 2005-11-23, 09:11 #1 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 23·3·101 Posts is there only one Mersenne prime that ends in 3? Sorry for the dumb queston. Is 22-1 the only Mersenne prime that ends in 3? Is it impossible for another Mersenne prime to end in 3? Just curious.
 2005-11-23, 09:16 #2 axn     Jun 2003 32·577 Posts Yes and Yes.
 2005-11-23, 09:26 #3 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 23·3·101 Posts Thanks.
 2005-11-23, 10:20 #4 Mystwalker     Jul 2004 Potsdam, Germany 3×277 Posts (Attempt of an) Explanantion: (1) 2^p-1 ends with a 3 iff p = 2 + 4*x with x >= 0 (2) For 2^p-1 to be prime, p has to be prime as well. But every suitable exponent is even, as stated in (1). The only even prime is 2.
 2005-11-23, 19:40 #5 ewmayer ∂2ω=0     Sep 2002 República de California 101101100111002 Posts Waiting for someone to ask if there are any Mersenne primes that end in 5...
2005-11-23, 20:38   #6
Wacky

Jun 2003
The Texas Hill Country

100010000012 Posts

Quote:
 Originally Posted by ewmayer Waiting for someone to ask if there are any Mersenne primes that end in 5...
How about the third Mersenne Prime?

You didn't specify the number base. Try the base represented by the decimal integer "26".

2005-11-23, 21:08   #7
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

101011000100112 Posts

Quote:
 Originally Posted by Wacky How about the third Mersenne Prime? You didn't specify the number base. Try the base represented by the decimal integer "26".
And, of course, all Mersenne primes beyond the second. Just choose the base appropriately.

Paul

2005-11-24, 02:10   #8
ewmayer
2ω=0

Sep 2002
República de California

1167610 Posts

Quote:
 Originally Posted by Wacky You didn't specify the number base. Try the base represented by the decimal integer "26".
By common convention, unless specified otherwise the base is presumed to be 10, Mr. Smartypants. ;)

Maybe we can get the crowd over at http://www.primegrid.com to try their hand at searching for the first-known Mersenne prime having the property that M(p) == 5 (modulo 10). *After* they've finished cracking RSA768 via brute-force trial division, naturally...

2005-11-24, 02:41   #9
Wacky

Jun 2003
The Texas Hill Country

32·112 Posts

Quote:
 Originally Posted by ewmayer Maybe we can get the crowd over at http://www.primegrid.com to try their hand at searching for the first-known Mersenne prime having the property that M(p) == 5 (modulo 10). *After* they've finished cracking RSA768 via brute-force trial division, naturally...
Well, now that you phrase it that way, it IS a task appropriate for the primegrid folks. However, I think that you are being a bit too restrictive on them. You should also be willing to accept any "not-yet-known" M. primes which have the property. ;)

2005-11-24, 19:33   #10
ewmayer
2ω=0

Sep 2002
República de California

22·3·7·139 Posts

Quote:
 Originally Posted by Wacky Well, now that you phrase it that way, it IS a task appropriate for the primegrid folks. However, I think that you are being a bit too restrictive on them. You should also be willing to accept any "not-yet-known" M. primes which have the property. ;)
I thought I'd give them something a bit easier, by way of warm-up. :P

 2005-11-25, 12:07 #11 Greenbank     Jul 2005 2×193 Posts I notice their core is still hideously inefficient. I wrote AND SENT THEM a 30 line GMP program which processed 1M candidate odd values in a matter of seconds (compared to theirs which took hours). They still aren't using it. Anyway, a speed up of almost 5 orders of magnitude still does nothing when the size of the search space is up around 10^100.

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