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 2005-01-06, 20:35 #12 Templus     Jun 2004 11010102 Posts You're right Geoff. I found a prime for 21380*5^50625+1 , which is equal to 4276*5^50626+1. But this doesn't mean that k=4276 doesn't have a prime for n less than 50626, so that's one thing that has to be checked!
2005-01-06, 21:22   #13
geoff

Mar 2003
New Zealand

13·89 Posts

Quote:
 Originally Posted by Templus I found a prime for 21380*5^50625+1 , which is equal to 4276*5^50626+1. But this doesn't mean that k=4276 doesn't have a prime for n less than 50626, so that's one thing that has to be checked!
Nice one!

It doesn't matter for the project whether or not k=4276 could have been eliminated by a smaller n than n=50626, any prime will do. The only problems are for k such as k=123910=5*24782. 24782 has already been eliminated because 24782*5^1+1 is prime, but this doesn't rule out the possibility that 123910*5^n+1 = 24782*5^(n+1)+1 is composite for all n. This means we have to leave k=123910 in the list.

Last fiddled with by geoff on 2005-01-06 at 21:22

 2005-01-06, 22:08 #14 geoff     Mar 2003 New Zealand 13·89 Posts OK the outcome of the observation by Templus is that all multiples of 5 can be eliminated except for 51460, 81700 and 123910, and Robert already found a prime for 81700. This means there are only 161 candidates left to test.
 2005-01-07, 19:39 #15 robert44444uk     Jun 2003 Oxford, UK 111011011112 Posts Results 4276*5^50626+1 4738*5^41656+1 5048*5^37597+1 5504*5^39475+1 are all PRP3. other checked to 2822 50057 3706 65328 5114 191771 Will now start on: 6082 6436 7528 8644 9248 Regards Robert Smith
2005-01-15, 03:02   #16
geoff

Mar 2003
New Zealand

13·89 Posts

Quote:
 Originally Posted by Templus Geoff, did you see that I reserved k = 24032 on the sixth of january?
Sorry I missed that, noted now.

My new results are: 33358*5^38096+1 and 33526*5^41142+1 are prime.

 2005-01-15, 12:27 #17 robert44444uk     Jun 2003 Oxford, UK 76F16 Posts Results to 10000 Searching for the remaining candidates k less than 10000 did not reveal any new prps: K largest n checked 6082 77402 6436 61512 7528 90216 8644 79150 9248 85471 Regards Robert Smith
 2005-01-15, 12:32 #18 robert44444uk     Jun 2003 Oxford, UK 11·173 Posts Reservations Geoff I will take candidates 110000-120000 next Regards Robert Smith
 2005-01-17, 21:03 #19 robert44444uk     Jun 2003 Oxford, UK 11×173 Posts Seriously big prime Now we are in business: http://primes.utm.edu/primes/page.php?id=73175 Primality testing 111502*5^134008+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Calling Brillhart-Lehmer-Selfridge with factored part 99.99% 111502*5^134008+1 is prime! (1503.0378s+0.0176s) First prime I have found for a while. It will be the 1000 to 1100 range of largest primes ever found, tantalisingly close to 100000 digits. Interestingly this is the k value which we might have expected to give the most problem having the smallest smallest Nash weight of all the remaining candidates! Regards Robert Smith
 2005-01-18, 08:52 #20 michaf     Jan 2005 479 Posts one down Hi there, My first prime for this project: PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8] Primality testing 37246*5^50452+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N-1 test using base 13 Calling Brillhart-Lehmer-Selfridge with factored part 99.99% 37246*5^50452+1 is prime! (456.9443s+0.0070s) Cheers, Micha Fleuren
 2005-01-24, 22:30 #21 michaf     Jan 2005 479 Posts One more down Hi all, I got one more down today, finding my second prime: PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8] Primality testing 38084*5^29705+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Calling Brillhart-Lehmer-Selfridge with factored part 99.98% 38084*5^29705+1 is prime! (65.7210s+0.0034s) Cheers, Micha
 2005-01-25, 19:43 #22 robert44444uk     Jun 2003 Oxford, UK 11·173 Posts The Riesel base 5 series I have taken a slight excursion away from Sierpinski base 5 to prepare the groundwork for the Riesel base 5 study. I have checked up to around n=12250 and I am still clearing 9-10 candidates a day. I will stop when sieving individual candidates makes sense. Right now there are 465 candidates left, so we should still work on the Sierpinski set. For the Sierpinski series, I have checked the following k to the following n with no primes: k n 110242 52766 110488 55772 And I have discovered: 111994 30446 is prp3 Regards Robert Smith

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