Sierpinski/Riesel Base 5: Post Primes Here

[Templus]

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!

[geoff]

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.

[geoff]

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.

[robert44444uk]

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

[geoff]

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.

[robert44444uk]

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

[robert44444uk]

Geoff

I will take candidates 110000-120000 next

Regards

Robert Smith

[robert44444uk]

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

[michaf]

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

[michaf]

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

[robert44444uk]

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