A166975 Four-digit primes such that, if the digits are ABCD, then AB+CD and A+B+C+D are also primes.

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

Offset

1,1

Comments

The last term of this sequence is a(179) = 9859.

Subsequence of A046704. - R. J. Mathar, Oct 28 2009

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

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..179 (full sequence)

Example

1217 is in the list since 1217, 12+17=29, and 1+2+1+7=11 are all primes.

Maple

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

Mathematica

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 *)

Prog

(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)]
print(afull[:42]) # Michael S. Branicky, Aug 20 2022

Crossrefs

Sequence in context: A107518 A073144 A131461 * A266369 A165295 A069489

Adjacent sequences: A166972 A166973 A166974 * A166976 A166977 A166978

Keyword

base,easy,fini,full,nonn

Author

Ray G. Opao, Oct 26 2009

Extensions

Numbers in the range 1000 to 1200 inserted by R. J. Mathar, Oct 28 2009

Many terms corrected by Nathaniel Johnston, Jun 03 2011

Status

approved