Talk:List of prime numbers

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 Template:Tl 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, ... (OEIS: A038134) 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#Two-sided 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 OEIS:A020994 agrees. Your sequence is OEIS: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 2^2n-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)

Twin Prime Goldbach Sequence

This combination is not even a conjecture. This combination is certainly wrong. In fact, it is impossible, to get every even number by adding any 2 consecutive odd numbers, no matter if they are primes or not, together. The smallest difference, that you can reach with 2 different sums each of 2 consecutive odd numbers, is 4. 1 + 3 = 4, 3 + 5 = 8, 5 + 7 = 12, 7 + 9 = 16, ...

The original Goldbach Conjecture states, that every even number greater than 2 is the sum of two prime numbers.

But, twin primes are specifically the primes with a gap of size 2. So, the sum of twin primes sequence is 8, 12, 24, 36, 60, 84, 120, 144, 204, 216, ... (OEIS: A054735) 94.31.89.138 (talk) 17:49, 17 September 2024 (UTC)

Split article?

The first section should be extracted to a new article — Template:TQ or just Template:TQ. Then the article should be renamed to Template:TQ or maybe Template:TQ or Template:TQ. Maybe create two new articles and keep this as a minimal index to the other two. — GhostInTheMachine ^{talk to me} 21:55, 17 December 2024 (UTC)