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a lucky prime. [3] the sum of five consecutive primes (7 + 11 + 13 + 17 + 19). a Heegner number. [4] a Pillai prime since 18! + 1 is divisible by 67, but 67 is not one more than a multiple of 18. [5] palindromic in quinary (232 5) and senary (151 6). a super-prime. (19 is prime) an isolated prime. (65 and 69 are not prime) a sexy prime with 61 ...
The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n. The tables show the multiplicity for each prime factor. ... 2·67 135: 3 ...
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.
The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of 5 ...
The original, called Mersenne's conjecture, was a statement by Marin Mersenne in his Cogitata Physico-Mathematica (1644; see e.g. Dickson 1919) that the numbers were prime for n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, and were composite for all other positive integers n ≤ 257.
1, 2, and 3 are not of the required form, so the Heegner numbers that work are 7, 11, 19, 43, 67, 163, yielding prime generating functions of Euler's form for 2, 3, 5, 11, 17, 41; these latter numbers are called lucky numbers of Euler by F. Le Lionnais. [4]
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The Euclid–Mullin sequence is an infinite sequence of distinct prime numbers, in which each element is the least prime factor of one plus the product of all earlier elements. They are named after the ancient Greek mathematician Euclid , because their definition relies on an idea in Euclid's proof that there are infinitely many primes , and ...