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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 discovery year and discoverer are of the Mersenne prime, since the perfect number immediately follows by the Euclid–Euler theorem. Discoverers denoted as "GIMPS / name" refer to GIMPS discoveries with hardware used by that person. Later entries are extremely long, so only the first and last six digits of each number are shown.
Margaret Petherbridge Farrar (March 23, 1897 – June 11, 1984) was an American journalist and the first crossword puzzle editor for The New York Times (1942–1968). Creator of many of the rules of modern crossword design, she compiled and edited a long-running series of crossword puzzle books – including the first book of any kind that Simon & Schuster published (1924). [1]
Times style is to always capitalize the first letter of a clue, regardless of whether the clue is a complete sentence or whether the first word is a proper noun. On occasion, this is used to deliberately create difficulties for the solver; e.g., in the clue [John, for one], it is ambiguous whether the clue is referring to the proper name John ...
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An odd prime p has irregular index n if and only if there are n values of k for which p divides B 2k and these ks are less than (p − 1)/2. The first irregular prime with irregular index greater than 1 is 157, which divides B 62 and B 110, so it has an irregular index 2. Clearly, the irregular index of a regular prime is 0.
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Random Thoughts & Interesting Things. CRAG (1A: Handhold on a free solo climb) A free solo climb is one done without ropes or other safety equipment, and is as dangerous as it sounds.
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