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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.
20 February 2024 4,665,949 58 37×2 15474010 + 1 8 November 2022 4,658,143 59 93839×2 15337656 – 1 28 November 2022 4,617,100 60 2 15317227 +2 7658614 + 1 31 July 2020 4,610,945 61 13×2 15294536 + 1 30 September 2023 4,604,116 62 6×5 6546983 + 1 13 June 2020 4,576,146 63 4788920×3 9577840 – 1 14 February 2024 4,569,798 64 69×2 14977631 ...
Falter used his friend, radio actor J. Scott Smart, as a model for Gramercy Park, the cover of the March 25, 1944 issue of The Saturday Evening Post. John Philip Falter (February 28, 1910 – May 20, 1982) was an American artist best known for his many cover paintings for The Saturday Evening Post.
For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1. [1] [2] The exponents p corresponding to Mersenne primes must themselves be prime, although the vast majority of primes p do not lead to Mersenne primes—for example, 2 11 − 1 = 2047 = 23 × 89. [3]
20.0 120 Jet engine: 100–30 m 6.32–200 110–140 Two-stroke chainsaw [26] 1 m 6.32 110 Jackhammer: 1 m 2.00 100 Traffic on a busy roadway (combustion engines) 10 m 0.20–0.63 80–90 Hearing damage (over long-term exposure, need not be continuous) [27] At ear 0.36 85 Passenger car (combustion engine) 10 m 0.02–0.20 60–80
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. If no exponent is written then the multiplicity is 1 (since p = p 1). The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined.
Linnik's theorem (1944) concerns the size of the smallest prime in a given arithmetic progression. Linnik proved that the progression a + nd (as n ranges through the positive integers) contains a prime of magnitude at most cd L for absolute constants c and L. Subsequent researchers have reduced L to 5.
73 has 37 as the mirroring of its decimal digits. 73 is the 21st prime number, and 37 the 12th. The "mirror property" is fulfilled when 73 has a mirrored permutation of its digits (37) that remains prime. Similarly, their respective prime indices (21 and 12) in the list of prime numbers are also permutations of the same digits (1, and 2).