Message boards : Number crunching : Sieve for palindromic primes?

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Message 144789 - Posted: 28 Oct 2020 | 18:48:23 UTC

While looking at new entries at T5K, I came across plindromic primes.

I find it interesting how these numbers are constructed, e.g. 10^(2n+1) - 10^n - 1 results in a number consisting of n 9s followed by a 1 followed by n 9s.

Some more examples can be found here.

Is there sieving software for these kind of numbers? The T5K entries all show openpfgw as software, no sieving software mentioned.
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Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

Message 144796 - Posted: 28 Oct 2020 | 20:56:02 UTC - in response to Message 144789.

Doing a lot of hunting on MersenneForums, Batalov indicated that the sieve he wrote was "quick n' dirty in Pari", PARI/GP being a mathematical programming/scripting language.

The reason that they are a little bit more convoluted (10^(2n)+999*10^(n-1)+1) is because if the form is too simple, it's liable to be divisible by numbers for a vast majority of exponents - see https://oeis.org/A187868 for a similar example.

I'm not certain on the precise particulars of how you'd quickndirty sieve in Pari. It looks to be a form that's a little more complicated than just figuring out what n lead to being non-prime for different p, like what you can do for k*b^n +- 1 with BSGS.[/url]

Message 144821 - Posted: 29 Oct 2020 | 18:50:23 UTC

Ok, thanks. I think I read something about GP/PARI in relation to plindromic primes, maybe in Prime pages comments on an entry?

I know enough to check some small numbers for primality using isprime(), but that's it. Unfortunately, what he calls quick'n'dirty for me probably is advanced math... :D

Maybe it's for the better, so I can keep focus on PG. And I already have a Proth prime side project (k in the 10^6 magnitude, so far away from anybody).
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Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

Message boards : Number crunching : Sieve for palindromic primes?