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A065727
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Primes p such that the decimal expansion of its base-9 conversion is also prime.
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75
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2, 3, 5, 7, 37, 43, 61, 109, 127, 199, 271, 277, 379, 457, 487, 523, 541, 613, 619, 673, 727, 757, 883, 907, 919, 991, 997, 1033, 1117, 1249, 1447, 1483, 1531, 1549, 1567, 1627, 1693, 1699, 1747, 1753, 1987, 2053, 2161, 2221, 2287, 2341, 2347, 2437, 2473
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OFFSET
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1,1
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COMMENTS
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In general rebase notation (Marc LeBrun): p9 = (9) [p] (10).
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LINKS
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EXAMPLE
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E.g., 997_10 = 1327_9 is prime, and so is 1327_10.
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MATHEMATICA
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Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 9]]] & ]
NestList[NestWhile[NextPrime, #, ! PrimeQ[FromDigits[IntegerDigits[#2, 9]]] &, 2] &, 2, 48] (* Jan Mangaldan, Jul 01 2020 *)
Select[Prime[Range[400]], PrimeQ[FromDigits[IntegerDigits[#, 9], 10]]&] (* Harvey P. Dale, Sep 19 2021 *)
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PROG
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(PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 9); if (isprime(b), write("b065727.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 28 2009
(PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 9))); \\ Michel Marcus, Jul 02 2020
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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