2004-09-28, 22:48 | #1 |
Jun 2003
Oxford, UK
2^{2}·3·7·23 Posts |
Sierpinski/Riesel Base 5: Post Primes Here
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:
2822 3706 4276 4738 5048 5114 5504 6082 6436 6772 7528 8644 9248 10918 12988 14110 15274 15506 15802 18530 21380 23690 24032 25240 25570 26798 27520 27676 29356 29914 30410 30658 31286 31712 32122 32180 32518 33358 33448 33526 33860 34094 36412 37246 37292 37328 37640 37714 37718 38084 40078 41738 42004 43018 43220 44134 44312 44348 44738 45652 45748 46240 46922 48424 49804 50192 51176 51208 51460 54590 55154 57316 58642 59302 59444 59912 60124 60394 60722 62698 64258 64940 66242 67282 67612 67748 68294 68416 68492 70550 71098 71492 74632 76246 76324 76370 76724 77072 77530 77908 78002 78398 79010 81556 81674 81700 82486 83032 83936 84032 84284 86354 89806 90056 90676 92158 92162 92182 92650 92906 93254 93374 93484 95246 96806 96994 98288 99784 99926 100898 101152 101284 102196 102482 104624 105166 105464 105754 106418 106588 106688 106900 107216 107258 108074 108308 109208 109988 110242 110488 110846 111382 111424 111502 111688 111994 113156 114158 117434 118388 118450 118568 120160 123406 123748 123910 125494 126134 126200 127312 127850 128432 128552 128896 129028 130324 131416 132028 133778 133990 135376 135526 136408 137132 137422 137600 137714 138022 138380 138514 138724 139196 139394 139606 139784 140498 141532 141578 143092 144052 144932 145982 146372 146780 149570 150506 150526 152050 152588 152836 153290 154222 156430 158044 158560 158696 159106 159128 159706 Last fiddled with by masser on 2008-09-15 at 17:28 Reason: Better Title |
2004-09-29, 18:54 | #2 |
Jun 2003
Oxford, UK
2^{2}·3·7·23 Posts |
5 less to look for
89038*5^18576+1
79010*5^18901+1 15802*5^18902+1 106588*5^18920+1 82486*5^19224+1 |
2004-10-06, 21:21 | #3 |
Jun 2003
Oxford, UK
78C_{16} Posts |
And more - 204 to go!
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 |
2004-10-07, 06:16 | #4 |
Jun 2003
Oxford, UK
2^{2}·3·7·23 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 |
Apr 2003
304_{16} Posts |
A first result using winpfgw (v1.2 rc1b)
159128*5^19709+1 Lars Last fiddled with by ltd on 2004-10-07 at 17:45 |
2004-10-11, 16:08 | #6 |
Jun 2003
Oxford, UK
2^{2}×3×7×23 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. 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 |
2004-10-27, 11:13 | #7 |
Mar 2003
New Zealand
2205_{8} Posts |
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. |
2004-12-26, 08:36 | #8 |
Mar 2003
New Zealand
13·89 Posts |
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. |
2004-12-26, 19:40 | #9 |
Apr 2003
2^{2}×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 |
Apr 2003
2^{2}·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: 159706*5^35244+1 is prime 158044*5^43818+1 is prime Lars |
2005-01-06, 10:41 | #11 |
Jun 2004
2×53 Posts |
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 Last fiddled with by Templus on 2005-01-06 at 10:43 |
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