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A prime can be a member of up to three prime triplets - for example, 103 is a member of (97, 101, 103), (101, 103, 107) and (103, 107, 109).When this happens, the five involved primes form a prime quintuplet.
All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
For example, the AP-3 {3, 7, 11} does not qualify, because 5 is also a prime. For an integer k ≥ 3, a CPAP-k is k consecutive primes in arithmetic progression. It is conjectured there are arbitrarily long CPAP's. This would imply infinitely many CPAP-k for all k. The middle prime in a CPAP-3 is called a balanced prime.
Construction of the Bell triangle. In mathematics, the Bell triangle is a triangle of numbers analogous to Pascal's triangle, whose values count partitions of a set in which a given element is the largest singleton.
The permutations that avoid the generalized patterns 12-3, 32-1, 3-21, 1-32, 3-12, 21-3, and 23-1 are also counted by the Bell numbers. [4] The permutations in which every 321 pattern (without restriction on consecutive values) can be extended to a 3241 pattern are also counted by the Bell numbers. [ 5 ]
Before Daniels gets to his prime, there’s a date in the NFC title game. Of course, he likes his chances, having advanced this far. Nothing about this situation seems too big for him.
It is no accident that each prime in a prime decade is displaced from its center by a power of 2, actually 2 or 4, since all centers are odd and divisible by both 3 and 5. A prime quadruplet can be described as a consecutive pair of twin primes, two overlapping sets of prime triplets, or two intermixed pairs of sexy primes. These "quad" primes ...
The triplets are on the same schedule, says Platsman. “Even if they’re napping and two wake up, we’ll wake up the third because it messes up your day if they’re all on different schedules ...