A059694
Primes p such that 1p1, 3p3, 7p7 and 9p9 are all primes.
Original entry on oeis.org
53, 2477, 4547, 5009, 7499, 8831, 9839, 11027, 24821, 26393, 29921, 36833, 46073, 46769, 47711, 49307, 53069, 59621, 64283, 66041, 79901, 84017, 93263, 115679, 133103, 151121, 169523, 197651, 207017, 236807, 239231, 255191, 259949, 265271, 270071, 300431, 330047
Offset: 1
53 is a term because 1531, 3533, 7537 and 9539 are primes.
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from sympy import isprime, nextprime
from itertools import islice
def agen(): # generator of terms
p = 2
while True:
sp = str(p)
if all(isprime(int(d+sp+d)) for d in "1379"):
yield p
p = nextprime(p)
print(list(islice(agen(), 40))) # Michael S. Branicky, Feb 23 2023
A059677
Numbers n such that 1n1, 3n3, 7n7 and 9n9 are all primes.
Original entry on oeis.org
20, 53, 341, 536, 2312, 2477, 3380, 3665, 3686, 4547, 5009, 5105, 6458, 6488, 6731, 6845, 7499, 7508, 7562, 7835, 8411, 8831, 9032, 9386, 9764, 9839, 11027, 11885, 14990, 19589, 20498, 21080, 22844, 24821, 25220, 26393, 27593, 29864, 29921
Offset: 1
2312 is a term because 123121, 323123, 723127 and 923129 are all primes.
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Select[ Range[ 30000 ], PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "1", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "3", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "7", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "9", {1, -1} ] ] ] & ]
enclose[n_]:=Table[FromDigits[Join[{i},IntegerDigits[n],{i}]],{i, {1,3,7,9}}]; Select[Range[30000],AllTrue[enclose[#],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 21 2015 *)
Showing 1-2 of 2 results.
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