# 14

This number is a composite.

10^{14} - 29 and 10^{14} - 27 are 14 digit twin primes. Note that 29 and 27 = 2 * 14 ± 1. [Luhn]

The smallest number such that (*n* + 3, *n* + 5, *n* + 17, *n* + 257, *n* + 65537) are all primes. Note that 3, 5, 17, 257 and 65537 are the known Fermat primes. [Russo]

The sum of the first 14 primes, the first 14 composites and the first 14 non-composites are each prime. (The sums are respectively: 281, 199 and 239). These sums are also simultaneously prime for the first 208, 214, 1148, 2460, 5558, 9922, 10658, 16738, 18886, 21734, 29370 and 30850 terms. [Caldwell]

The largest number for which there are as many composite numbers less than it as there are primes. [Murthy]

14 is the smallest semiprime whose reversal is a prime. [Gupta]

The smallest impossible value of Euler's Phi function. [Gupta]

1!*2!*3!*4!*5!*6!*7!*8!*9!*10!*11!*12!*13!*14! + 1 is prime. [Gupta]

14^14 plus the 14th prime is prime. Other smaller examples are 1, 2 and 4. [Gupta]

14 is the first number such that it and the next number are both the product of two distinct primes (14 = 2*7 and 15 = 3*5). [Axoy]

14 = π(1*4) * prime(1*4). Note that 14 is the smallest number with this property. [Firoozbakht]

1!*2!*3!*4!*5!*6!*7!*8!*9!*10!*11!*12!*13!*14! + prime(14) is prime. [Firoozbakht]

The concatenation of 14, the 1st and the 4th primes, is a prime whose sum of digits is 14. Note that the product of the 1st and the 4th primes is 14. [Silva]

The smallest number whose prime divisors sum to a square. [Silva]

14 = prime(1*4) + sigma(1*4). [Firoozbakht]

sigma(14) = (1*4)!. [Kumar]

The smallest semiprime whose distinct prime divisors sum to another semiprime. [Silva]

The smallest number whose sum and difference of the digits are twin primes. [Silva]

Prime(14)^14 - π(14) is prime. It is curious that the digits of 14 have the same property. [Firoozbakht]

The first multidigit prime difference between consecutive primes. See gaps between primes. [Silva]

14 is the smallest semiprime average of a semiprime number of first semiprimes, i.e., (4 + 6 + 9 + 10 + 14 + 15 + 21 + 22 + 25)/9 = 14. [Silva]

The only even brilliant number whose the reversal is prime. [Loungrides]

The reversal of 14 is the prime before the 14th prime. [Blankenship]

The smallest peculiar semiprime, i.e., a number that is the product of two primes whose concatenation (in some order) produce the decimal expansion of *e*, e.g., 14 = 2*7.
The sequence begins 14, 142, 22519844819412565193, 2244375512401258782637904641, 22443755124012587826379047223, 224437551240125878263790473657153479, ... . See the *largest known*. [Bajpai]

14 = 2*7 -> 2147 = 19*113 -> 192147113 = 857*224209. Note that each new semiprime begins and ends with the ordered factors of the previous one. Can you find a larger chain? See PC1807. [Honaker]

Lucas (14) + 14 and Lucas (14) - 14 are both prime. We note that the 14th Lucas number is 843 where both 843 +14 = 857 and 843 - 14 = 829 are prime. [Schiffman]