PRPs that are composites

[michaf]

In range 500-510, only one non-prime prp occured:

504725030*3^3-1 is prp
It factors as: 87011 * 156619
The next prime for the k is:
504725030*3^11-1

[henryzz]

should we be stopping using base 3 prp tests for base 3 conjectures
would that help the number of prps we are getting

[michaf]

I reckon it would reduce it a bit, but still, they will be there, and final tests will be needed, so no gain will be made overall.

[gd_barnes]

Originally Posted by michaf

I reckon it would reduce it a bit, but still, they will be there, and final tests will be needed, so no gain will be made overall.

I agree.

[gd_barnes]

Here's a question for the PRP/PSP gurus:

Is it possible to have a 3-PRP or "any" PRP for that matter that has more than 2 prime factors? Are there any examples?

I'm asking because we haven't found any with this effort.


Gary

[henryzz]

Originally Posted by gd_barnes

Here's a question for the PRP/PSP gurus:

Is it possible to have a 3-PRP or "any" PRP for that matter that has more than 2 prime factors? Are there any examples?

I'm asking because we haven't found any with this effort.


Gary

Originally Posted by XYYXF

(3^37159+1)/4 is divisible by 250154389. It was found by Henri Lifchitz as 3-PRP, but then a factor was discovered (by me).

is the remaining cofactor prp
if not yes to gary's question

[Jens K Andersen]

A007011: smallest pseudoprime to base 2 with n prime factors.

The base 3 sequence would start with 91, 286, 11011, 341341, 20821801.
Found with PARI/GP:
t=1;for(n=1,10^8,if(Mod(3,n)^(n-1)==1 && (b=bigomega(n))>t,\
print(n" "b" "factor(n));t=b))
91 2 [7, 1; 13, 1]
286 3 [2, 1; 11, 1; 13, 1]
11011 4 [7, 1; 11, 2; 13, 1]
341341 5 [7, 1; 11, 2; 13, 1; 31, 1]
20821801 6 [7, 1; 11, 2; 13, 1; 31, 1; 61, 1]

Change Mod(3,n) to use another base. It's inefficient so don't run for long.

[Flatlander]

Composite PRPs (with -f):
631020668*3^6-1 = 460014066971 = 570827 * 805873
631293542*3^3-1 = 17044925633 = 75377 * 226129
636386826*3^9-1 = 12526001896157 = 1615421 * 7754017

Lowest primes are:
631020668*3^41-1
631293542*3^26-1
636386826*3^17-1

[Flatlander]

Composite PRP:
682649738*3^4-1 = 55294628777 = 160637 * 344221

Lowest prime:
682649738*3^14-1

[MrOzzy]

I'm just wondering, is it also possible for a prime which isn't a prp using the current available tests?

[henryzz]

Originally Posted by MrOzzy

I'm just wondering, is it also possible for a prime which isn't a prp using the current available tests?

no