A058323 -id:A058323 - cp's OEIS frontend

A058362 Initial primes of sets of 6 consecutive primes in arithmetic progression.

121174811, 1128318991, 2201579179, 2715239543, 2840465567, 3510848161, 3688067693, 3893783651, 5089850089, 5825680093, 6649068043, 6778294049, 7064865859, 7912975891, 8099786711, 9010802341, 9327115723, 9491161423, 9544001791, 10101930253, 10523406343, 13193702321

Offset: 1

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

nonn

For all 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 CPAP-6 with common difference 60 starts at 293826343073 ~ 3*10^11, cf. A210727. [With a slope of a(n)/n ~ 5*10^8 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 CPAP-7. This must have a common difference >= 210. As of today, the smallest known CPAP-7 starts at 382003672700092872707633 ~ 3.8*10^23, cf. Andersen link. - M. F. Hasler, Oct 27 2018
The common difference of 60 first occurs at a larger-than-expected prime. The first CPAP-6 with common difference 90 starts at 8560443932347. The first CPAP-6 with common difference 120 starts at 1925601119017087. - Jerry M Lagrou, Jan 01 2024

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

Cf. A006560: first prime to start a CPAP-n.
Cf. A033451, A033447, A033448, A052242, A052243, A058252, A058323, A067388: start of CPAP-4 with common difference 6, 12, 18, ..., 48.
Cf. A054800: start of 4 consecutive primes in arithmetic progression (CPAP-4).
Cf. A052239: starting prime of first CPAP-4 with common difference 6n.
Cf. A059044: starting primes of CPAP-5.
Cf. A210727: starting primes of CPAP-5 with common difference 60.

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

Equals { A059044(i) | A059044(i+1) = A151800(A059044(i)) }, A151800 = nextprime. - M. F. Hasler, Oct 30 2018

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

A287547 Initial prime in set of 4 consecutive primes in arithmetic progression with difference 66.

Original entry on oeis.org

1140813701, 1314331181, 1729804331, 2615969891, 2765625631, 3827771821, 4266876641, 4348917061, 4700742041, 4845745831, 4877408441, 5311420901, 5395463741, 5409482081, 5693097391, 5816498981, 5902417331, 6173160871, 6692523011, 6914652461, 6960900641

Offset: 1

Zak Seidov, May 26 2017

nonn

Lars Blomberg, Table of n, a(n) for n = 1..10000

Analogous sequences [with common difference in square brackets]: A033451 [6], A033447 [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36], A058323 [42], A067388 [48], A259224 [54], A210683 [60].

More terms from Lars Blomberg, May 30 2017

A287550 Initial prime in set of 4 consecutive primes in arithmetic progression with difference 72.

Original entry on oeis.org

491525857, 1470227987, 2834347387, 4314407477, 4766711387, 6401372837, 6871241197, 8971400797, 10168905497, 11776429517, 11871902557, 14538547967, 14925896087, 15218517367, 15646776877, 15875854927, 17310026197, 17942416307, 18347931587, 19241492057, 19379888947

Offset: 1

Zak Seidov, May 26 2017

nonn

a(1)=491525857=A052239(12).

Chai Wah Wu, Table of n, a(n) for n = 1..100

from gmpy2 import is_prime, next_prime
A287550_list, p = [], 2
q, r, s = p+72, p+144, p+216
while s <= 10**10:
    np = next_prime(p)
    if np == q and is_prime(r) and is_prime(s) and next_prime(q) == r and next_prime(r) == s:
        A287550_list.append(p)
    p, q, r, s = np, np+72, np+144, np+216 # Chai Wah Wu, Jun 03 2017

a(8)-a(21) from Chai Wah Wu, Jun 03 2017

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A058362 Initial primes of sets of 6 consecutive primes in arithmetic progression.

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A287547 Initial prime in set of 4 consecutive primes in arithmetic progression with difference 66.

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A287550 Initial prime in set of 4 consecutive primes in arithmetic progression with difference 72.

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