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A255669
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Primes p such that p divides the concatenation of the next two primes.
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0
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OFFSET
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1,1
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COMMENTS
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No additional terms up to the 5-millionth prime. Is the sequence finite and complete?
No additional terms up to the billionth prime. - Chai Wah Wu, Mar 10 2015
a(5) > 10^18. If the reasonable assumption nextprime(p) < p + (log p)^2 holds, then a(5) > 10^53. However, the 192-digits prime
7046979865771812080536912751677852348993288590604026845637583892...
6174496644295302013422818791946308724832214765100671140939597315...
4362416107382550335570469798657718120805369127516778523489932887 is in the sequence. - Giovanni Resta, May 08 2015
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LINKS
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EXAMPLE
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The three primes beginning with 61 are 61, 67, and 71, and 61 evenly divides 6771.
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MATHEMATICA
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divQ[{a_, b_, c_}]:=Divisible[FromDigits[Flatten[IntegerDigits/@{b, c}]], a]; Transpose[Select[Partition[Prime[Range[500]], 3, 1], divQ]][[1]]
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PROG
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(Python)
from sympy import nextprime
A255669_list, p1, p2, l = [], 2, 3, 10
for n in range(10**8):
....p3 = nextprime(p2)
....if p3 >= l: # this test is sufficient by Bertrand-Chebyshev theorem
........l *= 10
....if not ((p2 % p1)*l + p3) % p1:
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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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