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14 (another Prime Pages' Curiosity) |
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will be down at times on those day (and possibly the next). (caldwell@utm.edu) 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!*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]
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