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.
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
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
Python
import numpy as np from functools import reduce def factors(n): return reduce(list._add_, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)) for i in range(1,50000): 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 len(factors(p1))<3 and len(factors(p3))<3 and len(factors(p7))<3 and len(factors(p9))<3: 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
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