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A065725
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Primes p such that the decimal expansion of its base-7 conversion is also prime.
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5
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2, 3, 5, 17, 29, 31, 43, 59, 71, 127, 157, 197, 211, 227, 239, 241, 337, 353, 367, 379, 409, 463, 491, 563, 577, 619, 647, 743, 757, 773, 787, 857, 911, 953, 967, 1093, 1123, 1163, 1193, 1249, 1303, 1373, 1429, 1459, 1471, 1499, 1583, 1597, 1613, 1627, 1669
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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): p7 = (7) [p] (10).
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LINKS
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EXAMPLE
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E.g., 787_10 = 2203_7 is prime, and so is 2203_10.
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MATHEMATICA
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Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 7]]] & ]
Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 7]]]&] (* Harvey P. Dale, Nov 10 2022 *)
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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, 7); if (isprime(b), write("b065725.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 27 2009
(PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 7), 10)); \\ Michel Marcus, Mar 05 2022
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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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