[QUOTE=Viliam Furik;560171]No, all those Mersenne numbers you listed have one factor and a (definitely) composite cofactor, so at least three factors.[/QUOTE]

I see, thanks for the explanation.:smile:

"PRP Cofactor" title is probably not the best choice of words then.

[QUOTE=a1call;560161]If I read the merssene.org correctly, M117239 has no known factors and F117239 is a (Probable) semiprime. So any complete list will have to be exclusively less than 117239.:smile:[/QUOTE]

A small notational quibble: doesn't [TEX]F_n[/TEX] typically denote the n-th Fermat number, i.e. [TEX]2^{2^n}+1[/TEX]?

I'm sure it does. I never hid the fact that I am no mathematician.
Thank you for the correction. I will try to remember the notation.:smile:

[QUOTE=a1call;560173]I see, thanks for the explanation.:smile:

"PRP Cofactor" title is probably not the best choice of words then.[/QUOTE]

It is, because if cofactor (the rest of the number, when divided by known certainly-prime factors) is PRP, then if the number has only one certainly-prime factor, it means it is most probably a semiprime.

If the cofactor is tested composite by PRP test, the cofactor is certainly composite.

If you refer to [URL="https://www.mersenne.org/report_exponent/?exp_lo=5807&exp_hi=&full=1"]this page[/URL], then yes, it may be kind of confusing to see PRP cofactor written there, but that's really only a title. If it would be PRP, for real, it would have had written "PRP_PRP_PRP_PRP_" in place of residue.