A347294 Primes that become semiprimes when turned upside down.
191, 691, 811, 991, 1009, 1069, 1619, 1801, 1861, 1889, 6089, 6869, 6911, 6961, 8101, 8191, 8609, 8669, 8689, 9001, 9811, 10009, 10099, 10111, 10169, 10181, 10601, 10889, 10891, 11119, 11161, 11689, 11699, 11801, 11969, 11981, 16061, 16691, 16699, 18089, 18119
Offset: 1
Examples
811 is a term because when 811 is turned upside down (rotated 180 degrees) it becomes 118=2*59, a semiprime.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
- C. K. Caldwell, and G. L. Honaker, Jr., Prime Curio for 191.
Programs
-
Mathematica
semiQ[n_] := PrimeOmega[n] == 2; q[n_] := PrimeQ[n] && Module[{d = IntegerDigits[n]}, AllTrue[d, MemberQ[{0, 1, 6, 8, 9}, #] &] && semiQ[FromDigits[Reverse[d] /. {6 -> 9, 9 -> 6}]]]; Select[Range[20000], q] (* Amiram Eldar, Jan 23 2022 *) -
Python
from sympy import isprime, factorint from itertools import count, islice, product def f(s): return s[::-1].translate({ord("6"):ord("9"), ord("9"):ord("6")}) def agen(): for digits in count(3): for first in "1689": for mid in product("01689", repeat=digits-2): for last in "19": s = first + "".join(mid) + last t = int(s) if isprime(t): flip = f(s) if sum(factorint(int(flip)).values()) == 2: yield t print(list(islice(agen(), 41))) # Michael S. Branicky, Feb 16 2024
Extensions
More terms from Amiram Eldar, Jan 23 2022
Comments