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%I #19 Aug 20 2022 13:38:14
%S 1013,1019,1031,1033,1051,1091,1093,1097,1217,1231,1259,1277,1291,
%T 1297,1433,1439,1453,1459,1493,1499,1613,1637,1657,1693,1697,1811,
%U 1871,2003,2027,2063,2069,2081,2083,2087,2089,2207,2221,2267,2281,2287,2423,2447
%N Four-digit primes such that, if the digits are ABCD, then AB+CD and A+B+C+D are also primes.
%C The last term of this sequence is a(179) = 9859.
%C Subsequence of A046704. - _R. J. Mathar_, Oct 28 2009
%C 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
%H Nathaniel Johnston, <a href="/A166975/b166975.txt">Table of n, a(n) for n = 1..179</a> (full sequence)
%e 1217 is in the list since 1217, 12+17=29, and 1+2+1+7=11 are all primes.
%p 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
%t 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 *)
%o (Python)
%o from sympy import isprime
%o def ok(n):
%o if n < 1000 or n > 9999 or not isprime(n): return False
%o return isprime(n//100 + n%100) and isprime(sum(map(int, str(n))))
%o afull = [k for k in range(1001, 10000, 2) if ok(k)]
%o print(afull[:42]) # _Michael S. Branicky_, Aug 20 2022
%K base,easy,fini,full,nonn
%O 1,1
%A _Ray G. Opao_, Oct 26 2009
%E Numbers in the range 1000 to 1200 inserted by _R. J. Mathar_, Oct 28 2009
%E Many terms corrected by _Nathaniel Johnston_, Jun 03 2011
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