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All integers are either even or odd. A square has even multiplicity for all prime factors (it is of the form a 2 for some a). The first: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 (sequence A000290 in the OEIS). A cube has all multiplicities divisible by 3 (it is of the form a 3 for some a).
The Goldbach conjecture verification project reports that it has computed all primes smaller than 4×10 18. [2] That means 95,676,260,903,887,607 primes [3] (nearly 10 17), but they were not stored. There are known formulae to evaluate the prime-counting function (the number of primes smaller than a given value) faster than computing the primes.
The decay time for a supermassive black hole of roughly 1 galaxy-mass (10 11 solar masses) due to Hawking radiation is on the order of 10 100 years. [7] Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol years in the future. A googol is considerably smaller than a centillion. [8]
The first 25 prime numbers (all the prime numbers less than 100) are: [9] 2, 3, ... (or all) prime factors is referred to as factorization of . It is ...
For Mersenne numbers, the trivial factors are not possible for prime n, so all factors are of the form 2kn + 1. In general, all factors of (b n − 1) /(b − 1) are of the form 2kn + 1, where b ≥ 2 and n is prime, except when n divides b − 1, in which case (b n − 1)/(b − 1) is divisible by n itself.
The third largest prime factor is greater than 100, [28] and less than . [29] N has at least 101 prime factors and at least 10 distinct prime factors. [21] [30] If 3 does not divide N, then N has at least 12 distinct prime factors. [31] N is of the form
The U.S. Preventive Services Task Force released a draft recommendation advising against using vitamin D to prevent falls and fractures in people over 60. Pharmacist Katy Dubinsky weighs in.
Year 100 was a leap year starting on Wednesday of the Julian calendar. The denomination 100 for this year has been used since the early medieval period.