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A210515
Numbers N such that concatenation of N, N, and x generates a prime for x=1 and x=3 and x=7 and x=9.
1
1235, 4061, 8255, 22775, 24665, 36500, 44501, 52343, 54434, 57644, 58109, 59567, 59588, 65018, 69407, 71789, 78689, 94280, 98594, 106748, 114272, 122504, 134369, 137129, 138905, 144302, 162236, 196439, 235808, 238235, 269912, 277919, 278633, 282461, 290534
OFFSET
1,1
COMMENTS
The primes generated are part of the sequences A210511, A210512, A210513 and A210514.
There are no terms N with d = 3, 9, 15, 21, ... decimal digits since in those cases (10^(d+1)+10) is divisible by 7. - Michael S. Branicky, Apr 28 2025
LINKS
MATHEMATICA
Select[Range[3*10^5], AllTrue[FromDigits/@Table[Join[IntegerDigits[#], IntegerDigits [#], {n}], {n, {1, 3, 7, 9}}], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 07 2021 *)
PROG
(Python)
from sympy import isprime
for i in range(1, 300000):
p1=int(str(i)+str(i)+"1")
p3=int(str(i)+str(i)+"3")
p7=int(str(i)+str(i)+"7")
p9=int(str(i)+str(i)+"9")
if isprime(p1) and isprime(p3) and isprime(p7) and isprime(p9):
print(i, end=', ')
(Python)
from gmpy2 import is_prime
def ok(n):
b = n*(10**len(str(n))+1)*10
return all(is_prime(b+x) for x in [1, 3, 7, 9])
print([N for N in range(3*10**5) if ok(N)]) # Michael S. Branicky, Apr 28 2025
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Abhiram R Devesh, Jan 26 2013
STATUS
approved