20200805, 11:50  #1 
Jul 2014
2^{2}·3·37 Posts 
module 2^p  1
Hi,
I understand the iteration sequence of the LucasLehmer test involves using module (2^p1) arithmetic. How do computers running these such a test cope with numbers with 20+ million digits? 
20200805, 13:07  #2 
Apr 2010
Over the rainbow
100101101001_{2} Posts 
one step at a time.

20200805, 13:30  #3  
Sep 2002
Database er0rr
110101000100_{2} Posts 
Quote:
For multiplication you use Fast Fourier Transforms (FFT). Some of the operations can be parallelized across available cores. Then there is making things cachefriendly. Last fiddled with by paulunderwood on 20200805 at 13:54 

20200805, 14:58  #4  
Jul 2014
2^{2}×3×37 Posts 
Thanks.
Quote:
I suppose you mean for calculating the squared term? 

20200805, 15:01  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{5}·179 Posts 
An appropriate search term might be "arbitrary precision arithmetic".

20200805, 15:06  #6 
Sep 2002
Database er0rr
2^{2}×3×283 Posts 

20200805, 22:38  #7 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
4419_{10} Posts 
More info on multiprecision multiplication at https://www.mersenneforum.org/showpo...21&postcount=7

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