20081123, 16:09  #23 
Jan 2005
111011111_{2} Posts 
In range 500510, only one nonprime prp occured:
504725030*3^31 is prp It factors as: 87011 * 156619 The next prime for the k is: 504725030*3^111 
20081123, 16:22  #24 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
3^{3}·7·31 Posts 
should we be stopping using base 3 prp tests for base 3 conjectures
would that help the number of prps we are getting 
20081123, 18:42  #25 
Jan 2005
479_{10} Posts 
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.

20081123, 21:17  #26 
May 2007
Kansas; USA
10347_{10} Posts 

20081123, 21:25  #27 
May 2007
Kansas; USA
3×3,449 Posts 
Here's a question for the PRP/PSP gurus:
Is it possible to have a 3PRP 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 
20081123, 21:43  #28  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
3^{3}·7·31 Posts 
Quote:
Quote:
if not yes to gary's question Last fiddled with by henryzz on 20081123 at 21:43 

20081123, 22:10  #29 
Feb 2006
Denmark
2×5×23 Posts 
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)^(n1)==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. 
20081125, 23:40  #30 
I quite division it
"Chris"
Feb 2005
England
31×67 Posts 
Composite PRPs (with f):
631020668*3^61 = 460014066971 = 570827 * 805873 631293542*3^31 = 17044925633 = 75377 * 226129 636386826*3^91 = 12526001896157 = 1615421 * 7754017 Lowest primes are: 631020668*3^411 631293542*3^261 636386826*3^171 
20081231, 21:33  #31 
I quite division it
"Chris"
Feb 2005
England
31·67 Posts 
Composite PRP:
682649738*3^41 = 55294628777 = 160637 * 344221 Lowest prime: 682649738*3^141 
20090319, 09:32  #32 
Apr 2008
Antwerp, Belgium
3×19 Posts 
I'm just wondering, is it also possible for a prime which isn't a prp using the current available tests?

20090319, 19:42  #33 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
3^{3}×7×31 Posts 

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