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A243767
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Decimal prime numbers which can be split into three equal-sized prime parts whose sum is prime. No leading zeros.
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1
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223, 227, 337, 353, 373, 557, 577, 733, 757, 773, 111119, 111317, 111323, 111337, 111347, 111373, 111731, 111773, 111779, 111913, 111953, 111959, 111973, 111997, 112337, 112397, 112913, 112919, 112967, 112997, 113111, 113117, 113131, 113147, 113159, 113161
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OFFSET
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1,1
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COMMENTS
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It appears that the sequence is infinite.
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LINKS
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EXAMPLE
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Prime number 112337 -> 11(prime) + 23(prime) + 37(prime) = 71(prime).
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MATHEMATICA
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Join[Select[FromDigits/@Select[Tuples[Prime[Range[4]], 3], PrimeQ[Total[ #]]&], PrimeQ], Select[ FromDigits[Flatten[IntegerDigits/@#]]&/@Select[ Tuples[ Prime[Range[5, 25]], 3], PrimeQ[Total[#]]&], PrimeQ]] (* The program generates the first 1283 terms of the sequence, i.e., all terms with six digits or less. *) (* Harvey P. Dale, Dec 04 2022 *)
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PROG
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(PARI) first(n) = { my(res = List()); for(i = 1, oo, pow10 = 10^i; pow100 = 100^i; forprime(p = 10^(i-1), 10^i, firstidigs = pow100 * p; forprime(q = 10^(i-1), 10^i, pandq = p+q; first2idigs = firstidigs + pow10*q; forprime(r = 10^(i-1), 10^i, if(isprime(pandq + r), c = first2idigs + r; if(isprime(c), listput(res, c); if(#res >= n, return(res) ) ) ) ) ) ) ) } \\ David A. Corneth, Dec 04 2022
(Python)
from sympy import isprime, primerange
from itertools import count, islice, product
def agen(): yield from filter(isprime, (a*10**(2*i) + b*10**i + c for i in count(1) for a, b, c in product(primerange(10**(i-1), 10**i), repeat=3) if isprime(a+b+c)))
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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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