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 2008-11-23, 16:09 #23 michaf     Jan 2005 479 Posts 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
 2008-11-23, 16:22 #24 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 5,743 Posts should we be stopping using base 3 prp tests for base 3 conjectures would that help the number of prps we are getting
 2008-11-23, 18:42 #25 michaf     Jan 2005 479 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.
2008-11-23, 21:17   #26
gd_barnes

May 2007
Kansas; USA

101000000000012 Posts

Quote:
 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.

 2008-11-23, 21:25 #27 gd_barnes     May 2007 Kansas; USA 72·11·19 Posts 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
2008-11-23, 21:43   #28
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

5,743 Posts

Quote:
 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
Quote:
 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

Last fiddled with by henryzz on 2008-11-23 at 21:43

 2008-11-23, 22:10 #29 Jens K Andersen     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)^(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.
 2008-11-25, 23:40 #30 Flatlander I quite division it     "Chris" Feb 2005 England 81D16 Posts 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
 2008-12-31, 21:33 #31 Flatlander I quite division it     "Chris" Feb 2005 England 31·67 Posts Composite PRP: 682649738*3^4-1 = 55294628777 = 160637 * 344221 Lowest prime: 682649738*3^14-1
 2009-03-19, 09:32 #32 MrOzzy     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?
2009-03-19, 19:42   #33
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

131578 Posts

Quote:
 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

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