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! 
[QUOTE=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![/QUOTE]
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. 
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.

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 
[QUOTE=Templus]Geoff, did you see that I reserved k = 24032 on the sixth of january?[/QUOTE]
Sorry I missed that, noted now. My new results are: 33358*5^38096+1 and 33526*5^41142+1 are prime. 
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 
Reservations
Geoff
I will take candidates 110000120000 next Regards Robert Smith 
Seriously big prime
Now we are in business:
[url]http://primes.utm.edu/primes/page.php?id=73175[/url] 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 
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 
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 
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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