Factors for unique exponents?

[science_man_88]

Originally Posted by Mr. P-1

Testing with composites is a waste of time. If Mp is divisable by a composite f, then it is divisable by the prime factors of f, and these will already have been found.

We nevertheless test some composites, because testing them to see if they are composite would take longer than testing to see if they divide Mp.

so x%6==5 ||x%6==1 is longer than MP%x==0.

[Mr. P-1]

Originally Posted by science_man_88

so x%6==5 ||x%6==1 is longer than MP%x==0.

25%6 == 1 but 25 is not prime.

In fact prime95 does eliminate all candidates /== 1 or 5 (mod 6), and a great many other more complex congruence classes guaranteed not to be prime. The remainder, which are then tested for divisibility into Mp, are not guaranteed to be prime.

[science_man_88]

Originally Posted by Mr. P-1

25%6 == 1 but 25 is not prime.

In fact prime95 does eliminate all candidates /== 1 or 5 (mod 6), and a great many other more complex congruence classes guaranteed not to be prime. The remainder, which are then tested for divisibility into Mp, are not guaranteed to be prime.

sorry didn't think there.

[LaurV]

Originally Posted by R.D. Silverman

I suggest that you study how TF is done now. Many of the trial factors
that are tested are not even prime. Think about why that is.

There is a very good explanation in this topic (my first points of my personal crank score on this forum).

[R.D. Silverman]

Originally Posted by Mr. P-1

Testing with composites is a waste of time. If Mp is divisable by a composite f, then it is divisable by the prime factors of f, and these will already have been found.

We nevertheless test some composites, because testing them to see if they are composite would take longer than testing to see if they divide Mp.

Bingo!