20180501, 07:37  #1 
Banned
"Luigi"
Aug 2002
Team Italia
2^{5}·149 Posts 
PArtial factorization of 2^8523486591
When This thread came out, I started some trivial trial factoring with Factor5, in the hope that a factor would appear and the claims of primality of the OP could be dismissed.
Meanwhile, the OP changed many times his claim, and the thread was finally locked. After that, I concluded my trialfactoring, but had no place to propagate its results, so I am publishing my results here in the faint hope to avoid the same waste of work (just about 9 GHz/day) to someone else (maybe either Aaron, James, Chris or George might be interested to update the general DB). Code:
Trialfactoring M852348659 in [2^1, 2^601] M852348659 has 0 factors in [2^1, 2^601]. Trialfactoring M852348659 in [2^60, 2^621] M852348659 has 0 factors in [2^60, 2^621]. Trialfactoring M852348659 in [2^62, 2^651] M852348659 has 0 factors in [2^62, 2^651]. Trialfactoring M852348659 in [2^65, 2^751] M852348659 has 0 factors in [2^65, 2^751]. Last fiddled with by ET_ on 20180501 at 07:46 
20180501, 12:35  #3  
Jun 2003
3×11^{2}×13 Posts 
Quote:
Quote:
Last fiddled with by axn on 20180501 at 12:36 

20180501, 15:33  #4 
"/X\(‘‘)/X\"
Jan 2013
B3C_{16} Posts 
I'll take it to 84 over the next 10 days or so.

20180501, 20:56  #5 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×2,399 Posts 

20180503, 17:19  #6 
"/X\(‘‘)/X\"
Jan 2013
2^{2}×719 Posts 
No factors < 2^81. I double checked everything below 2^80.
Work continues. Last fiddled with by Mark Rose on 20180503 at 17:20 
20180510, 15:37  #7 
"/X\(‘‘)/X\"
Jan 2013
2^{2}·719 Posts 

20180510, 16:28  #8  
Aug 2006
2^{2}×1,483 Posts 
Quote:
from before we did any work on the number. That's 1/8 the chance of being dealt a royal flush (in 5 cards). Or for the hold 'em fans, 40% the chance of being dealt a full house four times in a row. 

20180510, 18:27  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}×7×163 Posts 
Four times in a row? That's easy.

20180531, 10:34  #10 
Romulan Interpreter
Jun 2011
Thailand
5^{3}×71 Posts 
What? You missed few zeros here, or so... There are 52 cards in a pack and you randomly pick 5, you get one in C(52,5) chances to get the royal flush. This is like one in half million (edit: a bit less than 2 in a million (10^6)) or so... We played poker in our life and had royal flushes occasionally, but mersenne primes with exponents in 850M didn't find yet....
Last fiddled with by LaurV on 20180531 at 10:37 
20180531, 12:15  #11 
Aug 2006
1011100101100_{2} Posts 
That's the chance to get (for example) a royal flush in hearts, about 385 in 10^9. The chance to get any royal flush is 4 times larger, about 1539 in 10^9. You'd have to divide by 8 or 9 to be the same size as the probability I computed for M852348659.

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