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Old 2020-12-16, 02:28   #1
bhelmes's Avatar
Mar 2016

35510 Posts
Default a prime sieve for f(n)=n⁴+1

A peaceful night,

the sieve algorithm for the function f(n)=2n²-1 was too slow,
even with some improvements.

The function f(n)=n^p-1 increase too fast for practical use.

Does it make more sense to use a function like f(n)=n⁴+1
for a presieve for Mersenne numbers ?

The actual used presieve reduces 1/p primes for Mp, as far as I can see.

Two questions:
Is there an algorithm known for a prime sieve for the function f(n)=n⁴+1,
(from whom)

Does the t with t | f(n) grows faster and how fast.

Thanks in advance if you spend me some lines.

Greetings from corona time,

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Old 2020-12-16, 02:43   #2
VBCurtis's Avatar
Feb 2005
Riverside, CA

2×11×227 Posts

Originally Posted by bhelmes View Post
Does it make more sense to use a function like f(n)=n⁴+1
for a presieve for Mersenne numbers ?
No. We have a really good trial factoring algorithm, taking advantage of the fact that factors of Mersenne candidates are of form 2kp+1.
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