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 A269420 Record (maximal) gaps between primes of the form 8k + 3. 2
 8, 24, 32, 40, 48, 72, 120, 144, 152, 176, 216, 264, 320, 400, 520, 592, 600, 824, 856, 872, 936, 992, 1064, 1072, 1112, 1336, 1392, 1408, 1584, 1720, 2080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Dirichlet's theorem on arithmetic progressions suggests that average gaps between primes of the form 8k + 3 below x are about phi(8)*log(x). This sequence shows that the record gap ending at p grows almost as fast as phi(8)*log^2(p). Here phi(n) is A000010, Euler's totient function; phi(8)=4. Conjecture: a(n) < phi(8)*log^2(A269422(n)) almost always. A269421 lists the primes preceding the maximal gaps. A269422 lists the corresponding primes at the end of the maximal gaps. LINKS Alexei Kourbatov, On the distribution of maximal gaps between primes in residue classes, arXiv:1610.03340 [math.NT], 2016. Alexei Kourbatov, On the nth record gap between primes in an arithmetic progression, arXiv:1709.05508 [math.NT], 2017; Int. Math. Forum, 13 (2018), 65-78. Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019. EXAMPLE The first two primes of the form 8k + 3 are 3 and 11, so a(1)=11-3=8. The next prime of this form is 19; the gap 19-11 is not a record so nothing is added to the sequence. The next prime of this form is 43 and the gap 43-19=24 is a new record, so a(2)=24. PROG (PARI) re=0; s=3; forprime(p=11, 1e8, if(p%8!=3, next); g=p-s; if(g>re, re=g; print1(g", ")); s=p) CROSSREFS Cf. A007520, A269421, A269422. Sequence in context: A028644 A227175 A340930 * A056196 A044069 A028628 Adjacent sequences:  A269417 A269418 A269419 * A269421 A269422 A269423 KEYWORD nonn AUTHOR Alexei Kourbatov, Feb 25 2016 STATUS approved

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Last modified October 28 17:55 EDT 2021. Contains 348329 sequences. (Running on oeis4.)