PARI's commands

[3.14159]

Originally Posted by CRGreathouse

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

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.

[CRGreathouse]

Originally Posted by 3.14159

See the above. Must be at least a c90.

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?

Originally Posted by 3.14159

factors cannot be known to the user.

How do you determine this? Polygraph?

[3.14159]

Originally Posted by 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?

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.

Originally Posted by CRGreathouse

How do you determine this? Polygraph?

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

[kar_bon]

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

 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

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

[3.14159]

Originally Posted by Karsten

Until no others changes made so far. Check it.

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.

[Mini-Geek]

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

[kar_bon]

Originally Posted by Mini-Geek

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

Because it's his own list!

[3.14159]

Originally Posted by Mini-Geek

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

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^b - 1)
22. Twins.

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

[CRGreathouse]

Originally Posted by 3.14159

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.

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

Originally Posted by 3.14159

By the way: Last one is invalid, smallest factor must be p10.

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

[3.14159]

As opposed to 265134* 4549⁴⁵⁴⁹, I found a PRP for b = 4861 pretty soon:

240790 * 4861⁴⁸⁶¹ + 1 (17927 digits)

[3.14159]

Originally Posted by CRGreathouse

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

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

Originally Posted by CRGreathouse

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

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