Talk:List of prime numbers

Finiteness and infinitude of types of primes
I think it would be nice to note for some/all of the types of primes listed whether there are (proven) infinitely many such primes, (proven) finitely many, conjectured infinitely/finitely many, or unknown (no conjecture made, e.g. because there is no known heuristic suggesting finiteness or infinitude). Joel Brennan (talk) 14:10, 10 May 2022 (UTC)

What about 0?
What about 0? Like 1, 0 is neither prime or composite. Nate-Dawg921 (talk) 18:04, 23 November 2022 (UTC)
 * Right. I don't think this list should mention that. Many sources discuss whether 1 is prime but not 0. PrimeHunter (talk) 20:22, 23 November 2022 (UTC)
 * And what about -17? Or the square root of 2?  This article is only concerned with positive integers. JBL (talk) 21:07, 23 November 2022 (UTC)

Bi-Twin chains?
I think it would be nice to add bi-twin chains to the "List of primes by type" section, as they're notable enough to have their own separate Wiki page: https://en.wikipedia.org/wiki/Bi-twin_chain 63.192.65.2 (talk) 21:43, 20 December 2022 (UTC)


 * Sourced only to Weisstein and primenumbers.net, and a quick search doesn't suggest there's better sourcing out there waiting to be found. It seems super unlikely to me that it would survive an AfD. --JBL (talk) 21:53, 20 December 2022 (UTC)
 * I haven't really done an in-depth search, but I did find sourcing on Wolfram MathWorld (https://mathworld.wolfram.com/BitwinChain.html) and scientificlib (http://www.scientificlib.com/en/Mathematics/LX/BiTwinChain.html). I also found a cryptocurrency that searches for them (Primecoin, see: https://en.wikipedia.org/wiki/Primecoin). 63.192.65.2 (talk) 23:39, 20 December 2022 (UTC)
 * MathWorld is Weisstein. ScientificLib is a Wikipedia mirror.  Surely nothing needs to be said about the cryptocurrency.  That's exactly what I mean.  --JBL (talk) 00:39, 21 December 2022 (UTC)
 * Bi-twin chain is linked in Prime number classes at the bottom but has the same problem as the more notable Cunningham chain: It's a pattern of primes with different variations (the length) and not associated with a specific prime sequence like the other entries. Even if you only consider one length at a time, the natural sequence would not be primes but the even composite between the first twin primes. Bi-twin chain shows no sequence but only records. PrimeHunter (talk) 00:15, 21 December 2022 (UTC)

Semi-protected edit request on 20 February 2023
In the Cluster primes section, the following:

3, 5, 7, 11, 13, 17, 19, 23, ...

should be changed to:

3, 5, 7, 11, 13, 17, 19, 23, ... Boblyonsnj (talk) 23:37, 20 February 2023 (UTC)
 * Done, thanks. --JBL (talk) 00:05, 21 February 2023 (UTC)

unbounded Wall–Sun–Sun sequence
comparison example: Fibonacci

Fibonacci primes: 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917 (OEIS: A005478)

unbounded Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811 (OEIS: A000045)

What does the unbounded Wall–Sun–Sun sequence look like? 94.31.82.138 (talk) 19:17, 26 August 2023 (UTC)

There are only 9 two-sided primes.
There are only 9 two-sided primes.: 2, 3, 5, 7, 23, 37, 53, 73, 373

This is, because if you remove digits from both sides, 313, 317 and 3137 can be changed to 1, 797 and 3797 can be changed to 9 and 739397 can be changed to 3939, 939, 393, 93, 39 or 9. 2A00:6020:A123:8B00:E0DF:7AE2:ABD6:637 (talk) 19:23, 8 October 2023 (UTC)
 * List of prime numbers says "Primes that are both left-truncatable and right-truncatable". That includes 313, 317 and 3137. You don't have to be able to alternate between left and right. The listed source A020994 agrees. Your sequence is A085823 which is not called two-sided primes. PrimeHunter (talk) 01:39, 9 October 2023 (UTC)

new sequences
double Mersenne divisors

Primes p that divide 22 n-1 - 1, for some prime number 2n - 1.

7, 127, 62914441, 231733529, 2147483647, 64296354767, 338193759479, 5746991873407, 295257526626031, 87054709261955177, 242557615644693265201, 178021379228511215367151, 2106734551102073202633922471, 824271579602877114508714150039, 65997004087015989956123720407169, 170141183460469231731687303715884105727, 210206826754181103207028761697008013415622289

double Mersenne prime exponents

3, 7, 31, 127 94.31.84.138 (talk) 17:13, 25 October 2023 (UTC)

article protection
The article should be protected again.

[Edit=Require administrator access] (indefinite) [Move=Require administrator access] (indefinite) 94.31.83.138 (talk) 17:28, 29 October 2023 (UTC)


 * why Semen2 (talk) 16:06, 21 March 2024 (UTC)

missing left-truncatable primes
Some left-truncatable primes are missing.: 103, 107, 307, 503, 607, 907, 1013, 1097, 1103, ...

Left-truncatable primes are primes, that remain prime, when the leading decimal digit is successively removed. So, it does not matter, if some of its digits are zeros, as long as the digits on the right are another prime. A right-truncatable prime on the other hand can not include a zero in its digits.

updated list of left-truncatable primes: 2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 137, 167, 173, 197, 223, 283, 307, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 503, 523, 547, 607, 613, 617, ... 94.31.88.138 (talk) 19:52, 23 April 2024 (UTC)


 * If you were to follow the link either to the article Truncatable prime or to the referenced OEIS sequence, you would see that the definition explicitly forbids the digit 0. I would not be opposed to adding this to the article here. --JBL (talk) 21:46, 25 April 2024 (UTC)

new sequences part 2
part 1: https://en.wikipedia.org/w/index.php?title=Talk%3AList_of_prime_numbers&diff=1181856963&oldid=1179273429

The 4 sequences are combinations. Because "isolated primes" is defined as "Primes p such that neither p - 2 nor p + 2 is prime.", the combinations "isolated + sexy", "isolated + cousin" and "isolated + triplet" are all 3 possible. The last sequence are the primes, such that (p, p+2) are both happy primes, since these primes were not shown in The Happy Twin (with Ben Sparks) - Numberphile Podcast.

isolated sexy primes: 23, 37, 47, 53, 67, 79, 83, 89, 97, 113, 131, 157, 163, 167, 173, 223, 233, 251, 257, 263, 277, ...

isolated cousin primes: 23, 37, 47, 67, 79, 83, 97, 113, 127, 131, 163, 167, 223, 233, 277, ...

isolated triplet primes: 23, 37, 47, 67, 97, 113, 223, 233, 277, ...

happy twins: (3329, 3331), (6701, 6703), (14549, 14551), (30137, 30139), (31769, 31771), (44699, 44701), ... 2A00:6020:A123:8B00:685C:6384:5516:2C8A (talk) 20:05, 10 July 2024 (UTC)