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A206045 Numbers n such that 11 + j*n is prime for j = 0 to 10. 10
1536160080, 4911773580, 25104552900, 77375139660, 83516678490, 100070721660, 150365447400, 300035001630, 318652145070, 369822103350, 377344636200, 511688932650, 580028072610, 638663371710, 701534299830, 745828915650, 776625236100, 883476548850, 925639075620, 956863233690 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Original name: Values of the difference d for 11 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 10.

The computations were done without any assumptions on the form of d. 21st term is greater than 10^12.

All terms are multiples of 210=2*3*5*7. - Zak Seidov, May 16 2015

LINKS

Zak Seidov, Table of n, a(n) for n = 1..623

S. A. Khan, Primes in Geometric-Arithmetic Progression, arXiv preprint arXiv:1203.2083, 2012.

EXAMPLE

d =  4911773580 then {11, 4911773591, 9823547171, 14735320751, 19647094331, 24558867911, 29470641491, 34382415071, 39294188651, 44205962231, 49117735811} which is 11 primes in arithmetic progression.

MATHEMATICA

a = 11; Do[If[PrimeQ[{a, a + d, a + 2*d, a + 3*d, a + 4*d, a + 5*d, a + 6*d, a + 7*d, a + 8*d, a + 9*d, a + 10*d}] == {True, True, True, True, True, True, True, True, True, True, True}, Print[d]], {d, 210, 10^12, 210}] (* corrected by Zak Seidov, May 16 2015 *)

Select[Range[210, 10^12, 210], AllTrue[Range[0, 10]#+11, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 28 2016 *)

PROG

(PARI) is(n)=for(j=1, 10, if(!isprime(j*n+11), return(0))); 1 \\ Charles R Greathouse IV, May 18 2015

CROSSREFS

Cf. A040976, A206037, A206038, A206039, A206040, A206041, A206042, A206043, A206044.

Sequence in context: A157822 A034616 A084551 * A276820 A273815 A258885

Adjacent sequences:  A206042 A206043 A206044 * A206046 A206047 A206048

KEYWORD

nonn

AUTHOR

Sameen Ahmed Khan, Feb 03 2012

EXTENSIONS

New name from Charles R Greathouse IV, May 18 2015

STATUS

approved

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Last modified February 20 17:47 EST 2017. Contains 282392 sequences.