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A084482 Primes base 10 that remain primes in all nine bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers. 12

%I #15 Mar 25 2015 14:50:18

%S 50006393431,727533146383,2250332130313,2651541199513,4437592255351,

%T 4877749016143,6777899690983,7417899095713,7431376081543,

%U 7766799025303,9078654198463,10712216924641,12244626455491,13562282568103,14180813918071,14833027106593,19479075240913,19971686697103,23196986067193,34431442237963,36429184518721,49198998504223

%N Primes base 10 that remain primes in all nine bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers.

%C a(1) found by _Jack Brennen_ on Jul 13 2001; remaining terms computed by _Jack Brennen_, Nov 15 2001.

%C The number must end with 1, 3, 7, or 9 in each base from 2 to 10; thus must be congruent to: 1 (mod 2), 1 (mod 3), 1 or 3 (mod 4), 1 or 3 (mod 5), 1 (mod 6), 1 or 3 (mod 7), 1 or 3 or 7 (mod 8), 1 or 7 (mod 9), 1 or 3 or 7 or 9 (mod 10).

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_024.htm">PP and P Puzzle 24: Primes in several bases</a>

%o (PARI) isok(n) = sum(b=2, 10, isprime(subst(Pol(digits(n, b)), x, 10))) == 9; \\ _Michel Marcus_, Mar 22 2015

%Y Cf. A052026, A038537, A052027-A052033, A084482, A236356.

%K nonn,base,hard,nice

%O 1,1

%A _Jack Brennen_, Jun 29 2003

%E Thanks to _David W. Wilson_ for proposing the sequence and _W. Edwin Clark_ for verifying the terms using Maple's command isprime.

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)