20050106, 20:35  #12 
Jun 2004
2×53 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! 
20050106, 21:22  #13  
Mar 2003
New Zealand
13×89 Posts 
Quote:
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 20050106 at 21:22 

20050106, 22:08  #14 
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.

20050107, 19:39  #15 
Jun 2003
Oxford, UK
2,017 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 
20050115, 03:02  #16  
Mar 2003
New Zealand
13×89 Posts 
Quote:
My new results are: 33358*5^38096+1 and 33526*5^41142+1 are prime. 

20050115, 12:27  #17 
Jun 2003
Oxford, UK
3741_{8} 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 
20050115, 12:32  #18 
Jun 2003
Oxford, UK
11111100001_{2} Posts 
Reservations
Geoff
I will take candidates 110000120000 next Regards Robert Smith 
20050117, 21:03  #19 
Jun 2003
Oxford, UK
2,017 Posts 
Seriously big prime
Now we are in business:
http://primes.utm.edu/primes/page.php?id=73175 Primality testing 111502*5^134008+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 11 Calling BrillhartLehmerSelfridge 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 
20050118, 08:52  #20 
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 [N1, BrillhartLehmerSelfridge] Running N1 test using base 11 Running N1 test using base 13 Calling BrillhartLehmerSelfridge with factored part 99.99% 37246*5^50452+1 is prime! (456.9443s+0.0070s) Cheers, Micha Fleuren 
20050124, 22:30  #21 
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 [N1, BrillhartLehmerSelfridge] Running N1 test using base 2 Calling BrillhartLehmerSelfridge with factored part 99.98% 38084*5^29705+1 is prime! (65.7210s+0.0034s) Cheers, Micha 
20050125, 19:43  #22 
Jun 2003
Oxford, UK
2,017 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 910 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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