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A103523
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Concatenations of pairs of primes that differ by 100.
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5
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3103, 7107, 13113, 31131, 37137, 67167, 73173, 79179, 97197, 127227, 139239, 151251, 157257, 163263, 181281, 193293, 211311, 283383, 331431, 349449, 367467, 379479, 409509, 421521, 457557, 463563, 487587, 499599, 541641, 547647, 577677
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OFFSET
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1,1
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COMMENTS
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Integers in this sequence can never be prime, as, starting from the second one, they are all multiples of 3.
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LINKS
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FORMULA
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List: concatenate(p, p+100) iff p and p+100 are primes.
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EXAMPLE
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9191019 is in this sequence because 919 is prime, 919+100 = 1019 is prime and 9191019 is the concatenation of those two primes differing by 100.
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MAPLE
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f:= proc(n) if isprime(n) and isprime(n+100) then 10^(1+ilog10(n+100))*n+n+100 fi end proc:
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MATHEMATICA
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FromDigits[Join@@IntegerDigits/@{#, #+100}]&/@Select[Prime@Range@200, PrimeQ[#+100]&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)
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PROG
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(Python)
from sympy import isprime, primerange as prange
def auptop(lim):
return [int(str(p)+str(p+100)) for p in prange(2, lim+1) if isprime(p+100)]
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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