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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.
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω( n ) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS ).
The first part is a set of lettered clues, each of which has numbered blanks representing the letters of the answer. The second part is a long series of numbered blanks and spaces, representing a quotation or other text, into which the answers for the clues fit.
Find answers to the latest online sudoku and crossword puzzles that were published in USA TODAY Network's local newspapers. Puzzle solutions for Sunday, Dec. 1, 2024 Skip to main content
The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. [1] This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. [ 2 ]
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The last puzzle in "Pencilwise" has generally been "The World's Most Ornery Crossword," a large standard crossword puzzle which has two sets of clues spanning three pages. One set, which is revealed by folding one page in half to hide the second page, consists of "Hard" clues (three stars), while the clues under this fold are "Easy" (one star ...
For example, the odd integer 47 can be expressed as the sum of a prime and a semiprime in four different ways: 47 = 13 + 2×17 = 37 + 2×5 = 41 + 2×3 = 43 + 2×2. The number of ways this can be done is given by OEIS sequence A046927 (Number of ways to express 2n+1 as p+2q where p and q are primes). Lemoine's conjecture is that this sequence ...