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A262729 Strong (2,3,5,7)-primes. (See Comments for precise definition.) 11
2, 171472673, 343808687, 1364225981, 1469999801, 1871684753, 2110769237, 2227044401, 2411201729, 2485782361, 2545607453, 3795488227, 3946237717, 4213334953, 4395443513, 5308651577, 5770033901, 5832097819, 6385775491, 6694883219, 7064806421, 7235208829 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let V = (b(1), b(2), ..., b(k)), where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p a V-prime if the digits of p in base b(1) spell a prime in each of the bases b(2), ..., b(k). Call p a strong V-prime if p is a (b(j), ..., b(k))-prime for each of the tuples (b(j), ..., b(k)), for j = 1..k-1.

a(157) > 10^11. - Hiroaki Yamanouchi, Oct 25 2015

LINKS

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..156

EXAMPLE

Let p = 171472673. Confirmation that p is a strong (2,3,5,7)-prime follows.

Base-2 for p: u = (1,0,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,1);

u in base 3 spells the prime 8488002487771;

u in base 5 spells the prime 7749195106457425001;

u is base 7 spells the prime 67054080721013093290423.

Base-3 for p: v = (1, 0, 2, 2, 2, 1, 1, 2, 2, 2, 0, 1, 0, 2, 1, 2, 0, 2);

v in base 5 spells the prime 838940251427;

v in base 7 spells the prime 243692337097757.

Base-5 for p: w = (3, 2, 2, 3, 4, 4, 1, 1, 1, 1, 4, 3);

w in base 7 spells the prime 6598716743.

MATHEMATICA

{b1, b2, b3, b4} = {2, 3, 5, 7}; z = 10000000;

Select[Prime[Range[z]],

PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &&

PrimeQ[FromDigits[IntegerDigits[#, b1], b3]] &&

PrimeQ[FromDigits[IntegerDigits[#, b1], b4]] &&

PrimeQ[FromDigits[IntegerDigits[#, b2], b3]] &&

PrimeQ[FromDigits[IntegerDigits[#, b2], b4]] &&

PrimeQ[FromDigits[IntegerDigits[#, b3], b4]] &]

(* Peter J. C. Moses, Sep 27 2015 *)

CROSSREFS

Cf. A000040, A262727, A262728.

Sequence in context: A263645 A170998 A053823 * A034251 A230562 A170999

Adjacent sequences:  A262726 A262727 A262728 * A262730 A262731 A262732

KEYWORD

nonn,base

AUTHOR

Clark Kimberling, Oct 03 2015

EXTENSIONS

a(4)-a(22) from Hiroaki Yamanouchi, Oct 25 2015

STATUS

approved

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Last modified May 23 19:46 EDT 2017. Contains 286926 sequences.