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A166975
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Four-digit primes such that, if the digits are ABCD, then AB+CD and A+B+C+D are also primes.
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1
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1013, 1019, 1031, 1033, 1051, 1091, 1093, 1097, 1217, 1231, 1259, 1277, 1291, 1297, 1433, 1439, 1453, 1459, 1493, 1499, 1613, 1637, 1657, 1693, 1697, 1811, 1871, 2003, 2027, 2063, 2069, 2081, 2083, 2087, 2089, 2207, 2221, 2267, 2281, 2287, 2423, 2447
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listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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The last term of this sequence is a(179) = 9859.
Prime digit sums 5, 7, 11, 13, 17, 19, 23, 29, 31 occur 5, 8, 23, 19, 37, 37, 38, 9, 3 times, respectively. Sequence contains ten twin prime pairs. - Rick L. Shepherd, Feb 19 2013
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LINKS
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EXAMPLE
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1217 is in the list since 1217, 12+17=29, and 1+2+1+7=11 are all primes.
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MAPLE
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p:=1009: while p<10000 do d:=convert(p, base, 10): if(isprime(add(d[j], j=1..4)) and isprime(d[1]+d[3]+10*(d[2]+d[4])))then printf("%d, ", p): fi: p:=nextprime(p): od: # Nathaniel Johnston, Jun 03 2011
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MATHEMATICA
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apQ[n_]:=Module[{idn=IntegerDigits[n], a, b, c, d}, a=idn[[1]]; b=idn[[2]]; c= idn[[3]]; d=idn[[4]]; AllTrue[{10a+b+10c+d, Total[idn]}, PrimeQ]]; Select[ Prime[Range[PrimePi[1000]+1, PrimePi[9999]]], apQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 14 2015 *)
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PROG
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(Python)
from sympy import isprime
def ok(n):
if n < 1000 or n > 9999 or not isprime(n): return False
return isprime(n//100 + n%100) and isprime(sum(map(int, str(n))))
afull = [k for k in range(1001, 10000, 2) if ok(k)]
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CROSSREFS
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KEYWORD
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base,easy,fini,full,nonn
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AUTHOR
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EXTENSIONS
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Numbers in the range 1000 to 1200 inserted by R. J. Mathar, Oct 28 2009
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STATUS
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approved
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