1613 (another Prime Pages' Curiosity)
 Curios: Curios Search:   Participate: 1613^2 = 867253 + 867257 + 867259 (3 consecutive primes) = 25247 + 25253 + ... + 26251 + 26261 (101 consecutive primes). 1613 is a prime such that the previous two primes AND the next two primes are twin primes. There are 1613 prime sextuplets (p, p+4, p+6, p+10, p+12, p+16 all prime) < 10^10. 1613 is the 17th prime in the prime sequence f(n)=4*n^2 - 4*n + 653 (note that f(0), f(1), ... , f(16), f(17), f(18) are all primes, while f(19) is not). (760*10^1613 - 31)/9 = 8 (4)1613 1 is prime (note the 1613 consecutive 4's in the middle). Given p2=1613 and the previous prime p1=1609 it is curious that p1^2+p2^3 +/- 1 is a twin prime pair. 82^1613 - 81^1613 is prime. 1613 is the smallest 4 digit prime that starts a run of 6 consecutive primes where between primes exactly one digit changes and where the resulting digits may be permuted: (i.e., 1613, 1619, 1621, 1627, 1637, 1657). 1613 is the largest prime factor of 2^26+1. (1613) = M(8); (1613) + 2*1613 is a perfect square of a prime (59^2). (In case it is not obvious, 1613 is one of my favorite small 4-digit primes not related to the Mersenne primes. :-)) [Noll] (There is one curio for this number that has not yet been approved by an editor.)   To link to this page use http://primes.utm.edu/curios/page.php?number_id=9044 Prime Curios! © 1999-2013 (all rights reserved)