
View Poll Results: Predict the number of digits from within the factor for M1277  
<=90 digits  1  5.00%  
91105 digits  0  0%  
106120 digits  0  0%  
121135 digits  7  35.00%  
136150 digits  2  10.00%  
151165 digits  2  10.00%  
166180 digits  3  15.00%  
181193 digits (since M1277 has 385 digits, it cannot be more than 193 digits)  1  5.00%  
has 3 prime factors  3  15.00%  
has >=4 prime factors  1  5.00%  
Voters: 20. You may not vote on this poll 

Thread Tools 
20191006, 00:52  #1 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3650_{10} Posts 
Predict the number of digits from within the factor for M1277
With the smaller factor of M1061 found, let's guess that of M1277 (predict the number of digits)

20191006, 03:49  #2 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·1,153 Posts 
What is the Mersenne number with a prime exponent which has the highest known number of prime factors?

20191006, 05:20  #3  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3^{3}×5×37 Posts 
Quote:


20191006, 19:41  #4 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×1,153 Posts 
Fantastic query.
Thank you. 
20191009, 08:16  #5 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10100000000110_{2} Posts 
We had a similar guess thread for M1061 where we (royal we) hit the "3 factors" cdot. We were far away in the woods, and at the time we voted we knew that we work against the probability, but it was "cute" to have a 3way split, and not many people voted it, so that is why. With how much ECM was done here, and how many prime candidates for the factor (i.e. there are more "large" primes than "small" primes, fighting for the "largest factor" honours), the best chances is still a split which is as much uneven as possible. That would mean the smallest factor somewhere at 120 digits or so. But we didn't vote yet. Still thinking about...
On the other hand, chances to have less than 100 digits are almost nonexistent, as well as the chances for a 4way split (it would mean that the smallest factor is under 96 digits, most probably under 75 or so, considering that we won't have a 4brilliant). Edit: voted... but OTOH, we are thinking to edit the poll to make the voter's name visible once you voted (as we had other polls in the past). Otherwise, how can I prove that I was right and you were wrong? Last fiddled with by LaurV on 20191009 at 08:25 
20191014, 19:01  #6 
"Rashid Naimi"
Oct 2015
Remote to Here/There
902_{16} Posts 
Probably obvious to some but hopefully not to all here are some pointers which are absolutely of no use for factoring M1277.
* As with any Mersenne number Mq with a prime exponent, M1277 has at least one prime factor p where valuation(p1,2) = 1 * As with any composite Mersenne numberMq with a prime exponent, M1277 has at least one factor a = Mq/p where valuation(a1,2) > 1 * As with any composite Mersenne number Mq with a prime exponent, M1277 has at least one prime factor p and a factor a = Mq/p coprime to p where valuation(p^21,2) = valuation(a^21,2) > 2 * As with any composite Mersenne number Mq with a prime exponent, M1277 has at least one prime factor p and a factor a = Mq/p coprime to p where valuation((p.a)^21,2) = q+1 = 1278 Last fiddled with by a1call on 20191014 at 19:26 Reason: mQ 
20191014, 21:42  #7  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3^{3}·5·37 Posts 
Quote:
φ(1441)/φ(131)φ(11) primitive cofactor = p64 * p64 * p66 * p80 Not really a miss. Nearly a 4brilliant :) There is a first time for anything. 

20220611, 11:04  #8 
"University student"
May 2021
Beijing, China
269 Posts 
I guess 160 digits (about 2^530). Might be larger than the factor of M1061.
(Seems that we haven't found a Mersenne prime factor larger than 2^500 yet) 
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