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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). The largest prime in the first 4digit cousin prime pair (p, q) such that p^2+q^3 /+1 is a twin prime pair. 82^1613  81^1613 is prime. 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 4digit primes not related to the Mersenne primes. :)) [Noll]
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