Talk:Palindromic prime

attention

if any one has a short logic for printing a series of palindromic number please write it down here. — Preceding unsigned comment added by 101.63.186.134 (talk) 17:13, 21 February 2012 (UTC)

Density of palindromic primes

The following seems obvious to me, but I can't think of a good source.

The density of palindromic primes, among numbers n with an odd number of digits, is conjectured to be asymtotically

${\ln n}^{-2}\prod _{p|{b^{2}-1}}{(1-1/p)}^{-1}$

—The preceding unsigned comment was added by Arthur Rubin (talk • contribs) .

That looks familiar. A very similar formula might appear in Ribenboim's prime Guiness. I'll post tomorrow on this. PrimeFan 22:59, 5 July 2006 (UTC)

I was mistaken, it's not in Ribenboim's book. I looked at Mathworld, which quotes Banks (2004):

$P(x)~O({{N(x)lnlnlnx} \over {lnlnx}})$

Next I looked at the article on palindromic primes by Ondrejka and Dubner in J. Recr. Math. 26(4), which has plenty of concrete numbers but no formulas. PrimeFan 23:01, 6 July 2006 (UTC)

infinitely many palindromic primes

"It is not known if there are infinitely many palindromic primes in base 10" seems to conflict with "it is known that, for any base, almost all palindromic numbers are composite". Either there is only a cofinite set of palindrome primes (i.e. allmost all palindrome numbers are composite), or there may be an infinite number of palindrome primes, or I'm misunderstanding something (which is why I write on the discussion page instead of editing the article). It would be great if anybody more fluent in number theory than me could resolve this... —Preceding unsigned comment added by 93.104.69.237 (talk) 11:29, 4 October 2010 (UTC)

"Almost all" is a technical term in mathematics. In this case, although the reference would have to be checked (both for what it says and for its reliability, I think it's saying that the limit as n goes to infinity of the number of palindromic primes less than n to the number of palindromes less than n is 0. — Arthur Rubin (talk) 15:48, 4 October 2010 (UTC)

Right. The article says "it is known that, for any base, almost all palindromic numbers are composite". Note there is a link on almost all. Wikipedia articles often link terms to another article explaining more about them although the precise meaning here is not explicitly explained in almost all. PrimeHunter (talk) 22:20, 4 October 2010 (UTC)

Except that almost all integers are composite in general, for the right mathematical definition of "almost all". So is this saying anything more restrictive? 67.151.97.194 (talk) 01:08, 21 May 2014 (UTC)

I haven't seen the paper but as stated here, it's not more restrictive than for all integers. But it's still worth mentioning that it holds for palindromes in any base. It's what most people would probably have guessed, but it had to be proved. There are many other integer sequences where it's expected but hasn't been proved that almost all numbers are composite. PrimeHunter (talk) 23:15, 21 May 2014 (UTC)

Since there are many definitions of "almost all" it should be made precise in the article which is meant here. --Jobu0101 (talk) 16:28, 15 February 2015 (UTC)

I have added an explanation.[1] PrimeHunter (talk) 17:17, 15 February 2015 (UTC)

Thank you. --Jobu0101 (talk) 19:36, 15 February 2015 (UTC)

Larger palindromic primes does exist at larger bases above 10^10^100, decimal primes at tetrational levels or above (maybe >10^10^10^...^10^10^10) too! However, these larger primes are not yet known. 2405:9800:BA31:F6:FD7E:6343:96DA:9CBD (talk) 05:56, 4 September 2021 (UTC)

Longest palindromic prime

Longest palindromic prime updated Jan 2024 - https://t5k.org/top20/page.php?id=53

I don’t know math well enough to confidently edit the article sorry

2600:1700:F4D1:D70:8435:B49C:FA7A:E19E (talk) 01:37, 31 May 2024 (UTC)