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Old 2020-01-23, 17:21   #5
paulunderwood's Avatar
Sep 2002
Database er0rr

2·11·149 Posts

Originally Posted by storm5510 View Post
I was learning to use the ABC2 input type for PFGW early this morning when I came up with these:

10*2^13509-1 is 3-PRP! (0.0290s+0.0015s)
10*2^21737-1 is 3-PRP! (0.0676s+0.0011s)
10*2^25623-1 is 3-PRP! (0.0805s+0.0011s)
I am not sure about the meaning of "3-" in this instance. I know how to calculate the number of digits in 2p-1. How that translates to something in this format, I do now know.

These are roughly 4200, 7000 and 8500 digits. You can get the exact values with pari/GP with length(decimal(10*2^13509-1)).

"3-PRP" means it passes Fermat's Little Theorem test: 3^(N-1)=1 mod N, which is necessary but not sufficient for a prime. With PFGW you can specify small bases with the -b switch.
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