20051123, 09:11  #1 
Bemusing Prompter
"Danny"
Dec 2002
California
2×3×397 Posts 
is there only one Mersenne prime that ends in 3?
Sorry for the dumb queston.
Is 2^{2}1 the only Mersenne prime that ends in 3? Is it impossible for another Mersenne prime to end in 3? Just curious. 
20051123, 09:16  #2 
Jun 2003
4,967 Posts 
Yes and Yes.

20051123, 09:26  #3 
Bemusing Prompter
"Danny"
Dec 2002
California
2·3·397 Posts 
Thanks.

20051123, 10:20  #4 
Jul 2004
Potsdam, Germany
3·277 Posts 
(Attempt of an) Explanantion:
(1) 2^p1 ends with a 3 iff p = 2 + 4*x with x >= 0 (2) For 2^p1 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. 
20051123, 19:40  #5 
∂^{2}ω=0
Sep 2002
República de California
2^{4}·727 Posts 
Waiting for someone to ask if there are any Mersenne primes that end in 5...

20051123, 20:38  #6  
Jun 2003
The Texas Hill Country
1089_{10} Posts 
Quote:
You didn't specify the number base. Try the base represented by the decimal integer "26". 

20051123, 21:08  #7  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
2×3×13×137 Posts 
Quote:
Paul 

20051124, 02:10  #8  
∂^{2}ω=0
Sep 2002
República de California
2^{4}·727 Posts 
Quote:
Maybe we can get the crowd over at http://www.primegrid.com to try their hand at searching for the firstknown Mersenne prime having the property that M(p) == 5 (modulo 10). *After* they've finished cracking RSA768 via bruteforce trial division, naturally... 

20051124, 02:41  #9  
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
Quote:


20051124, 19:33  #10  
∂^{2}ω=0
Sep 2002
República de California
2^{4}×727 Posts 
Quote:


20051125, 12:07  #11 
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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