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Old 2008-11-23, 16:09   #23
michaf
 
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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
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Old 2008-11-23, 16:22   #24
henryzz
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should we be stopping using base 3 prp tests for base 3 conjectures
would that help the number of prps we are getting
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Old 2008-11-23, 18:42   #25
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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.
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Old 2008-11-23, 21:17   #26
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Quote:
Originally Posted by michaf View Post
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.
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Old 2008-11-23, 21:25   #27
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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
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Old 2008-11-23, 21:43   #28
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Quote:
Originally Posted by gd_barnes View Post
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 View Post
(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
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Old 2008-11-23, 22:10   #29
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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.
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Old 2008-11-25, 23:40   #30
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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
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Old 2008-12-31, 21:33   #31
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Composite PRP:
682649738*3^4-1 = 55294628777 = 160637 * 344221

Lowest prime:
682649738*3^14-1
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Old 2009-03-19, 09:32   #32
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I'm just wondering, is it also possible for a prime which isn't a prp using the current available tests?
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Old 2009-03-19, 19:42   #33
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Quote:
Originally Posted by MrOzzy View Post
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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