20210409, 07:26  #1 
"Nigel"
Apr 2021
10100_{2} Posts 
Factorize a 129digit number
Code:
167385405371362584782846408982573842467658758597134437038484622185119073107121016763971211022426995195588062521818021967340171529 Last fiddled with by Dr Sardonicus on 20210423 at 13:54 
20210409, 07:47  #2 
"Nigel"
Apr 2021
20_{10} Posts 
First factor estimate
Maybe it has 45 digits or so in the first factor

20210409, 07:50  #3 
Jul 2003
So Cal
2^{2}×3×5^{2}×7 Posts 
It looks like you are perhaps trying to factor this number?
Code:
33765749444723236975938383549571694531728722961303548619829414070181324100^2+1 
20210409, 07:52  #4 
"Nigel"
Apr 2021
2^{2}·5 Posts 
yes I am and I accidentally stumbled on this crap

20210409, 12:55  #5 
Apr 2020
13·23 Posts 
Normally when I stumble across some crap I want to clean it up, not find its factors.
But if you desperately want to know the factors of this number, the best way is to find them yourself. There's some excellent advice in this thread, particularly post #8, assuming you're running Windows. A 129digit number should take less than a day to factor using yafu+ggnfs on a modern quadcore. 
20210409, 19:35  #6 
Aug 2006
3·1,993 Posts 
Let s = 33765749444723236975938383549571694531728722961303548619829414070181324100 so your number is s^2 + 1.
Is there some special significance to s or s^2 + 1? 
20210409, 20:23  #7 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3·11^{2}·17 Posts 

20210409, 21:44  #8 
"Rashid Naimi"
Oct 2015
Remote to Here/There
13×157 Posts 
Code:
33765749444723236975938383549571694531728722961303548619829414070181324100^2+1 = 6811381392746490569 x 167385405371362584782846408982573842467658758597134437038484622185119073107121016763971211022426995195588062521818021967340171529 ETA: PARIGP code: Code:
factor(6811381392746490569 ) %8 = [ 109 1] [ 23917 1] [2612774911073 1] Last fiddled with by a1call on 20210409 at 22:13 
20210409, 22:50  #9  
"Rashid Naimi"
Oct 2015
Remote to Here/There
13·157 Posts 
Quote:


20210409, 23:14  #10  
Apr 2020
13·23 Posts 
Quote:
The factors of OP's number are Code:
166447885293942400205064657834447096885456111524808377 1005632514199652040245190989819182186076324308468303514078693528739687994577 Both factors are 1 mod 8. 

20210410, 01:44  #11 
"Nigel"
Apr 2021
2^{2}×5 Posts 
Thanks
Thanks for the new 54digit factor!

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