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Message boards : Number crunching : Sieve for palindromic primes?

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Joined: 25 Feb 20
Posts: 410
ID: 1241833
Credit: 188,069,752
RAC: 995,366
321 LLR Amethyst: Earned 1,000,000 credits (1,058,073)Cullen LLR Amethyst: Earned 1,000,000 credits (1,169,946)ESP LLR Amethyst: Earned 1,000,000 credits (1,128,885)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,148,593)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Amethyst: Earned 1,000,000 credits (1,248,861)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Amethyst: Earned 1,000,000 credits (1,060,324)SGS LLR Amethyst: Earned 1,000,000 credits (1,152,105)TRP LLR Amethyst: Earned 1,000,000 credits (1,039,866)Woodall LLR Amethyst: Earned 1,000,000 credits (1,129,385)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Amethyst: Earned 1,000,000 credits (1,045,010)AP 26/27 Ruby: Earned 2,000,000 credits (2,470,273)WW Double Bronze: Earned 100,000,000 credits (161,280,000)GFN Turquoise: Earned 5,000,000 credits (7,149,778)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
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.
____________
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)

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Discovered 2 mega primesFound 1 prime in the 2018 Tour de PrimesFound 2 primes in the 2020 Tour de PrimesFound 2 primes in the 2021 Tour de Primes321 LLR Bronze: Earned 10,000 credits (38,954)ESP LLR Gold: Earned 500,000 credits (942,185)PPS LLR Double Silver: Earned 200,000,000 credits (284,953,062)PSP LLR Silver: Earned 100,000 credits (489,641)SoB LLR Jade: Earned 10,000,000 credits (12,960,428)SR5 LLR Jade: Earned 10,000,000 credits (10,694,695)SGS LLR Gold: Earned 500,000 credits (563,819)TRP LLR Jade: Earned 10,000,000 credits (12,767,693)321 Sieve (suspended) Silver: Earned 100,000 credits (395,205)PPS Sieve Double Silver: Earned 200,000,000 credits (229,814,554)TRP Sieve (suspended) Gold: Earned 500,000 credits (669,191)AP 26/27 Sapphire: Earned 20,000,000 credits (25,547,717)WW Double Amethyst: Earned 1,000,000,000 credits (1,301,268,000)GFN Emerald: Earned 50,000,000 credits (79,577,076)PSA Ruby: Earned 2,000,000 credits (3,025,234)
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]

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Joined: 25 Feb 20
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ID: 1241833
Credit: 188,069,752
RAC: 995,366
321 LLR Amethyst: Earned 1,000,000 credits (1,058,073)Cullen LLR Amethyst: Earned 1,000,000 credits (1,169,946)ESP LLR Amethyst: Earned 1,000,000 credits (1,128,885)Generalized Cullen/Woodall LLR Amethyst: Earned 1,000,000 credits (1,148,593)PPS LLR Amethyst: Earned 1,000,000 credits (1,225,852)PSP LLR Amethyst: Earned 1,000,000 credits (1,248,861)SoB LLR Amethyst: Earned 1,000,000 credits (1,669,219)SR5 LLR Amethyst: Earned 1,000,000 credits (1,060,324)SGS LLR Amethyst: Earned 1,000,000 credits (1,152,105)TRP LLR Amethyst: Earned 1,000,000 credits (1,039,866)Woodall LLR Amethyst: Earned 1,000,000 credits (1,129,385)321 Sieve (suspended) Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Amethyst: Earned 1,000,000 credits (1,045,010)AP 26/27 Ruby: Earned 2,000,000 credits (2,470,273)WW Double Bronze: Earned 100,000,000 credits (161,280,000)GFN Turquoise: Earned 5,000,000 credits (7,149,778)PSA Amethyst: Earned 1,000,000 credits (1,022,470)
Message 144821 - Posted: 29 Oct 2020 | 18:50:23 UTC
Last modified: 29 Oct 2020 | 18:51:06 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)

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Message boards : Number crunching : Sieve for palindromic primes?

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