F14 is the smallest composite Fermat number with no known factor.
1014 - 29 and 1014 - 27 are 14 digit twin primes. Note that 29 and 27 = 2 x 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 = prime(1) * prime(4). Note that 14 is the smallest
number with this property. [Firoozbakht]
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 =  (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]
There are 14 primes formed from distinct prime digits. [Silva]
The first integer of the only pair of consecutive numbers,
whose prime divisors are four consecutive primes. [Silva]
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]
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