Sierpinski/Riesel Base 5: Post Primes Here

robert44444uk · 2004-09-28, 22:48

I have been looking for the lowest Sierpinski and Riesel numbers base 5. In the y*hoo primeform group you will see posts about it.

The lowest even Reisel number is mooted to be 346802 and the lowest even Sierpinski 159986. That is to say 346802.5^n-1 is always composite for every n, and 159986.5^n+1 is similarly endowed.

The Sierpinskis look the easiest to look at. We have to show there is a prime for every even k (in the power series k.5^n+1) less than k=159986 and I have checked so far up to n=18468 for all of the remaining values of k shown below. All other values of k have a prime at less than n=18468

If anyone wants to take a stab at any of the values then reserve a k by answering this thread and run it up to a certain value of n, and post either the prp or the range tested.

As usual, I will not be able to take a terribly active role in all of this, I have no computer power and work takes up a lot of my time right now.

Regards to all of the mersenneforum

Robert Smith

Code:

robert44444uk · 2004-09-29, 18:54

89038*5^18576+1
79010*5^18901+1
15802*5^18902+1
106588*5^18920+1
82486*5^19224+1

robert44444uk · 2004-10-06, 21:21

81700*5^20040+1
89806*5^20852+1
95246*5^21669+1
132028*5^21736+1
138022*5^22280+1
141532*5^22472+1

The size of these first-time prp numbers is getting interesting and only 204 candidates to check.

Regards

Robert Smith

robert44444uk · 2004-10-07, 06:16

Actually have not started sieving yet! Just pre factoring ( -f100) in pfgw. Populations of candidates with no factors under 1000000 are only 1-3% or so in any case.

Don't know of a quick way to sieve 200 candidates, Phil Carmody developed software to sieve 12 at a time.

But it would be easy to take a few candidates and sieve in NewPGen and run up to 200000 or so.

Regards

Robert Smith

PS: 150506*5^22667+1 popped up overnight

ltd · 2004-10-07, 17:45

A first result using winpfgw (v1.2 rc1b)

159128*5^19709+1

Lars

robert44444uk · 2004-10-11, 16:08

Lars and other interested folk:

I have been away for a few days, and the following are all first primes - sorry for the one over 150000, I shall stop testing these.

150506*5^22667+1
33860*5^23213+1
6772*5^23214+1
104624*5^23443+1
137714*5^23863+1
96806*5^24813+1
106418*5^25077+1
59302*5^25228+1

All remaining candidates are tested to n=25228. After these and Lars's discovery there are 195 remaining candidates.

I will take on the first 12 of the remainder and check to n=200000, namely

2822
3706
4276
4738
5048
5114
5504
6082
6436
7528
8644
9248

Regards

Robert Smith

geoff · 2004-10-27, 11:13

I found the following two primes:

15274*5^31410+1
15506*5^39203+1

These four k have no primes for n < 50000:

10918
12988
14110
18530

I am going to stop there for now.

geoff · 2004-12-26, 08:36

I found these two primes: 30658*5^29860+1, 31286*5^59705+1 (196 to go).

These two k have no primes for n < 60000, so I'm releasing them: 30410, 31712.

I'm reserving the following six k: 32122, 32180, 32518, 33358, 33448, 33526.

ltd · 2004-12-26, 19:40

Hi,

finally there is a new report from my side.
I have checked my logs and found that i did forget to test k=153290 upto n=30000 and guess what i found:

153290*5^29859+1 is prime!!!!!

I keep my other k reserved.

Lars

ltd · 2005-01-02, 08:36

OK here are the results from my search.

All k are tested to n=50000. I will unreserve these k for now.

And here comes the important part:

159706*5^35244+1 is prime
158044*5^43818+1 is prime

Lars

Templus · 2005-01-06, 10:41

In the case that 21380*5^n+1 equals to 4276*5^(n+1)+1 , the following are prime:

4276*5^50626+1
21380*5^50625+1
106900*5^50624+1

Shouldn't we remove all multiples of 10 (which are multiples of 5) which have duplicate k's in the list? Like the k I mentioned above?

2822 / 14110 / 70550
18530 / 92650
4738 / 23690 / 118450
5114 / 25570 / 127850
5504 / 27520 / 137600
6082 / 30410 / 152050
6436 / 32180
6772 / 33860

And so on....The most left number is the 'base' number and the numbers following it are multiples of 5 of it. So why would we check for their primality, if we new the primality of a multiple of it?

Am I right? (Just a n00b on primality)

Also, I'm now reserving k = 24032 until n=100000

2004-09-29, 18:54	#2
robert44444uk Jun 2003 Suva, Fiji 2·1,021 Posts	5 less to look for 890385^18576+1 790105^18901+1 158025^18902+1 1065885^18920+1 82486*5^19224+1

2004-10-06, 21:21	#3
robert44444uk Jun 2003 Suva, Fiji 2·1,021 Posts	And more - 204 to go! 817005^20040+1 898065^20852+1 952465^21669+1 1320285^21736+1 1380225^22280+1 1415325^22472+1 The size of these first-time prp numbers is getting interesting and only 204 candidates to check. Regards Robert Smith

2004-10-07, 06:16	#4
robert44444uk Jun 2003 Suva, Fiji 2×1,021 Posts	Sieve Actually have not started sieving yet! Just pre factoring ( -f100) in pfgw. Populations of candidates with no factors under 1000000 are only 1-3% or so in any case. Don't know of a quick way to sieve 200 candidates, Phil Carmody developed software to sieve 12 at a time. But it would be easy to take a few candidates and sieve in NewPGen and run up to 200000 or so. Regards Robert Smith PS: 150506*5^22667+1 popped up overnight

2004-10-07, 17:45	#5
ltd Apr 2003 2²×193 Posts	A first result using winpfgw (v1.2 rc1b) 1591285^19709+1 Lars Last fiddled with by ltd on 2004-10-07 at 17:45*

2004-10-11, 16:08	#6
robert44444uk Jun 2003 Suva, Fiji 11111111010₂ Posts	Some more Lars and other interested folk: I have been away for a few days, and the following are all first primes - sorry for the one over 150000, I shall stop testing these. 1505065^22667+1 338605^23213+1 67725^23214+1 1046245^23443+1 1377145^23863+1 968065^24813+1 1064185^25077+1 593025^25228+1 All remaining candidates are tested to n=25228. After these and Lars's discovery there are 195 remaining candidates. I will take on the first 12 of the remainder and check to n=200000, namely 2822 3706 4276 4738 5048 5114 5504 6082 6436 7528 8644 9248 Regards Robert Smith

2004-10-27, 11:13	#7
geoff Mar 2003 New Zealand 10010000101₂ Posts	I found the following two primes: 152745^31410+1 155065^39203+1 These four k have no primes for n < 50000: 10918 12988 14110 18530 I am going to stop there for now.

2004-12-26, 08:36	#8
geoff Mar 2003 New Zealand 13×89 Posts	I found these two primes: 306585^29860+1, 312865^59705+1 (196 to go). These two k have no primes for n < 60000, so I'm releasing them: 30410, 31712. I'm reserving the following six k: 32122, 32180, 32518, 33358, 33448, 33526.

2004-12-26, 19:40	#9
ltd Apr 2003 2²·193 Posts	Hi, finally there is a new report from my side. I have checked my logs and found that i did forget to test k=153290 upto n=30000 and guess what i found: 153290*5^29859+1 is prime!!!!! I keep my other k reserved. Lars

2005-01-02, 08:36	#10
ltd Apr 2003 2²×193 Posts	OK here are the results from my search. All k are tested to n=50000. I will unreserve these k for now. And here comes the important part: 1597065^35244+1 is prime 1580445^43818+1 is prime Lars

2005-01-06, 10:41	#11
Templus Jun 2004 2·53 Posts	In the case that 213805^n+1 equals to 42765^(n+1)+1 , the following are prime: 42765^50626+1 213805^50625+1 1069005^50624+1 Shouldn't we remove all multiples of 10 (which are multiples of 5) which have duplicate k's in the list? Like the k I mentioned above? 2822 / 14110 / 70550 18530 / 92650 4738 / 23690 / 118450 5114 / 25570 / 127850 5504 / 27520 / 137600 6082 / 30410 / 152050 6436 / 32180 6772 / 33860 And so on....The most left number is the 'base' number and the numbers following it are multiples of 5 of it. So why would we check for their primality, if we new the primality of a multiple of it? Am I right? (Just a n00b on primality) Also, I'm now reserving k = 24032 until n=100000 Last fiddled with by Templus on 2005-01-06 at 10:43*

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