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The tables contain the prime factorization of the natural numbers from 1 to 1000. ... An odd number does not have the prime factor 2. The first: 1, 3, 5, 7, 9, 11, 13 ...
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. This has been used to compute that there are 1,925,320,391,606,803,968,923 primes (roughly 2 × 10 21) smaller ...
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m , for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).
(The numbers 18 and 20 also have six factors but are much larger.) Ten, in contrast, only has four factors, which are 1, 2, 5, and 10, of which 2 and 5 are prime. [37] Six shares the prime factors 2 and 3 with twelve; however, like ten, six only has four factors (1, 2, 3, and 6) instead of six. Its corresponding base, senary, is below the DSA's ...
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000. A group of one thousand units is sometimes known, from Ancient Greek, as a chiliad. [1]
If all e i ≡ 1 (mod 3) or 2 (mod 5), then the smallest prime factor of N must lie between 10 8 and 10 1000. [41] More generally, if all 2e i +1 have a prime factor in a given finite set S, then the smallest prime factor of N must be smaller than an effectively computable constant depending only on S. [41]
To put in perspective the size of a googol, the mass of an electron, just under 10 −30 kg, can be compared to the mass of the visible universe, estimated at between 10 50 and 10 60 kg. [5] It is a ratio in the order of about 10 80 to 10 90 , or at most one ten-billionth of a googol (0.00000001% of a googol).
[7] [8] [9] It is widely believed, [10] but not proven, that no odd perfect numbers exist; numerous restrictive conditions have been proven, [10] including a lower bound of 10 1500. [11] The following is a list of all 52 currently known (as of January 2025) Mersenne primes and corresponding perfect numbers, along with their exponents p.