[QUOTE=CRGreathouse]That's fine -- but I still think we need a good way to judge the (prior) difficulty of finding a factorization.
[/QUOTE]

See the above. Must be at least a c90, and it cannot be divisible by any prime smaller than 10 digits, and factors cannot be known to the user.

[QUOTE=3.14159;227453]See the above. Must be at least a c90.[/QUOTE]

So how do you rank two different factorizations? Say, a p30 . p70 vs. a p25 . p80? What about a p31 . p64? What about a p20 . p81? What about a p9 . p30 . p65?

[QUOTE=3.14159;227453]factors cannot be known to the user.[/QUOTE]

How do you determine this? Polygraph?

[QUOTE=CRGreathouse]So how do you rank two different factorizations? Say, a p30 . p70 vs. a p25 . p80? What about a p31 . p64? What about a p20 . p81? What about a p9 . p30 . p65?
[/QUOTE]

Simple: Semiprimes are most impressive, and it is also more impressive when the primes are evenly sized, differing in size by about 4-10 digits. By the way: Last one is invalid, smallest factor must be p10.

[QUOTE=CRGreathouse]How do you determine this? Polygraph?[/QUOTE]

Again, if you're willing to fake ECM/SIQS/NFS data, show me how.

I've tried to simplify the list in post #1011:

[code]
1. k*2^n+-1 Proth/Riesel
2. k*b^n+-1 Generalized Proth/Riesel
3. k*b!^n+-1 Factorial-based Proth/Riesel
4. k*b#^n+-1 Primorial-based Proth/Riesel
5. k*b^n+-1 Prime-based Proth/Riesel, b>2 prime
6. k*n#+-1 Primorial
7. k*n!+-1 Factorial
8. n*b^n+-1 Generalized Cullen/Woodall
9. n*b^n+-1 Factorial Cullen/Woodall, b Factorial
10. n*b^n+-1 Primorial Cullen/Woodall, b Primorial
11. n*b^n+-1 Prime-based Cullen/Woodall, b prime
12. k*b^b+-1 k-b-b, k<b^b
13. k*b^b+-1 k-b-b, b Factorial, k<b^b
14. k*b^b+-1 k-b-b, b Primorial, k<b^b
15. k*b^b+-1 k-b-b, b prime, k<b^b
16. 4-group n^1+1, n^2+1, n^4+1 primes
17. Factorization of form #1-#16, #digits>=90
18. Factorization not of form #1-#16, #digits>=90
19. k*b^n+c General arithmetic progressions, c>100 prime; #digits>=2000
20. k*b^n-1, k*b^n+1 Twins.

NOTE:
- n>1, b>1
[/code]

3.14159 searches only for +1-side on #1-#19.

[QUOTE=Karsten]Until no others changes made so far. Check it.
[/QUOTE]

Replace Special and General Cofactor with Factorization, also add that the smallest prime factor must be a p10 and the number must at minimum be a c90.

Why are there no k*b^n-1?

[QUOTE=Mini-Geek;227461]Why are there no k*b^n-1?[/QUOTE]

Because it's his own list! :smile:

[quote=Mini-Geek]Why are there no k*b^n-1?[/quote]

I knew one of you was going to complain about the -1 thing.

Other members only:

20. n-1 analogues of Proths.
21. n-1 analogues of k-b-b, (k * b[sup]b[/sup] - 1)
22. Twins.

I stay within 1-19. Ban me for a week if I defy that rule.

[QUOTE=3.14159;227456]Simple: Semiprimes are most impressive, and it is also more impressive when the primes are evenly sized, differing in size by about 4-10 digits. By the way: Last one is invalid, smallest factor must be p10.[/QUOTE]

"Semiprimes are most impressive": Does this mean that a p20 . p70 is better than a p80 . p80 . p80?

[QUOTE=3.14159;227456]By the way: Last one is invalid, smallest factor must be p10.[/QUOTE]

Yes, that was intentional. I'm amused that a p20 . p70 qualifies while a p9 . p90 . p90 does not.

As opposed to 265134* 4549[sup]4549[/sup], I found a PRP for b = 4861 pretty soon:

240790 * 4861[sup]4861[/sup] + 1 (17927 digits)

[QUOTE=CRGreathouse]"Semiprimes are most impressive": Does this mean that a p20 . p70 is better than a p80 . p80 . p80?
[/QUOTE]

Okay: Large composites with prime factors no smaller than 50 digits are more impressive.

[QUOTE=CRGreathouse]Yes, that was intentional. I'm amused that a p20 . p70 qualifies while a p9 . p90 . p90 does not.
[/QUOTE]

Well, factorization cannot have any restrictions then, except the number must be at least a c90. Factor restriction lifted.