

A058362


Initial primes of sets of 6 consecutive primes in arithmetic progression.


6



121174811, 1128318991, 2201579179, 2715239543, 2840465567, 3510848161, 3688067693, 3893783651, 5089850089, 5825680093, 6649068043, 6778294049, 7064865859, 7912975891, 8099786711, 9010802341, 9327115723, 9491161423
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

For all of the terms listed so far, the common difference is equal to 30. These are the smallest such sets.
It is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression. As of December 2000 the record is 10 primes.
All terms are congruent to 9 mod 14.  Zak Seidov, May 03 2017
The first CPAP6 with common difference 60 starts at 293826343073 ~ 3e11, cf. A210727. [With a slope of a(n)/n ~ 5e8 this would correspond to n ~ 600.] This sequence consists of first members of pairs of consecutive primes in A059044. Conversely, a pair of consecutive primes in this sequence starts a CPAP7. This must have a common difference >= 210. As of today, the smallest known CPAP7 starts at 382003672700092872707633 ~ 3.8e23, cf. Andersen link.  M. F. Hasler, Oct 27 2018


LINKS

Zak Seidov, Table of n, a(n) for n = 1..102
Jens K. Andersen, The Largest Known CPAP's, updated Sept. 2018
OEIS wiki, Consecutive primes in arithmetic progression, updated Jan. 2020
Index entries for sequences related to primes in arithmetic progressions


FORMULA

Found by exhaustive search for 6 primes that are in arithmetic progression with all other intermediate numbers being composite.
A058362 = { A059044(i)  A059044(i+1) = A151800(A059044(i)) }, A151800 = nextprime.  M. F. Hasler, Oct 30 2018


PROG

(PARI) p=c=g=P=0; forprime(q=1, , p+g==(p+=g=qp) next; q==P+2*g&& c++ c=3; c>5&& print1(P3*g, ", "); P=qg) \\ M. F. Hasler, Oct 26 2018


CROSSREFS

Cf. A006560: first prime to start a CPAPn.
Cf. A033451, A033447, A033448, A052242, A052243, A058252, A058323, A067388: start of CPAP4 with common difference 6, 12, 18, ..., 48.
Cf. A054800: start of 4 consecutive primes in arithmetic progression (CPAP4).
Cf. A052239: starting prime of first CPAP4 with common difference 6n.
Cf. A059044: starting primes of CPAP5.
Cf. A210727: starting primes of CPAP5 with common difference 60.
Sequence in context: A250458 A038131 A081734 * A213463 A175321 A215264
Adjacent sequences: A058359 A058360 A058361 * A058363 A058364 A058365


KEYWORD

nonn


AUTHOR

Harvey Dubner (harvey(AT)dubner.com), Dec 18 2000


EXTENSIONS

Corrected by Jud McCranie, Jan 04 2001
a(11)a(18) from Donovan Johnson, Sep 05 2008
Split off comment from name to clarify definition.  M. F. Hasler, Oct 27 2018


STATUS

approved



