PRPs that are composites - Page 3

michaf · 2008-11-23, 16:09

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 · 2008-11-23, 16:22

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

michaf · 2008-11-23, 18:42

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 · 2008-11-23, 21:17

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.

gd_barnes · 2008-11-23, 21:25

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 · 2008-11-23, 21:43

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

Jens K Andersen · 2008-11-23, 22:10

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 · 2008-11-25, 23:40

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 · 2008-12-31, 21:33

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

Lowest prime:
682649738*3^14-1

MrOzzy · 2009-03-19, 09:32

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

henryzz · 2009-03-19, 19:42

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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2008-11-23, 16:09	#23
michaf Jan 2005 111011111₂ Posts	In range 500-510, only one non-prime prp occured: 5047250303^3-1 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) 3³·7·31 Posts	should we be stopping using base 3 prp tests for base 3 conjectures would that help the number of prps we are getting

2008-11-23, 18:42	#25
michaf Jan 2005 479₁₀ 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, 21:25	#27
gd_barnes May 2007 Kansas; USA 3×3,449 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, 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 31×67 Posts	Composite PRPs (with -f): 6310206683^6-1 = 460014066971 = 570827 805873 6312935423^3-1 = 17044925633 = 75377 226129 6363868263^9-1 = 12526001896157 = 1615421 7754017 Lowest primes are: 6310206683^41-1 6312935423^26-1 636386826*3^17-1

2008-12-31, 21:33	#31
Flatlander I quite division it "Chris" Feb 2005 England 31·67 Posts	Composite PRP: 6826497383^4-1 = 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?