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The first 1000 primes are listed below, ... Primes p for which p − 1 divides the square of the product of all earlier terms. 2, 3, 5, 7, ...
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 first: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 (sequence A000578 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p. As of 2024, there are 52 known Mersenne primes (and therefore perfect numbers), the largest 18 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search, or GIMPS. [2]
Powerful numbers are also known as squareful, square-full, or 2-full. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers powerful . The following is a list of all powerful numbers between 1 and 1000:
Super Bowl Squares are the second most popular office sports betting tradition in the United States (No. 1: March Madness brackets), maybe because the outcome is based entirely on luck.
The sum of one odd square and one even square is congruent to 1 mod 4, but there exist composite numbers such as 21 that are 1 mod 4 and yet cannot be represented as sums of two squares. Fermat's theorem on sums of two squares states that the prime numbers that can be represented as sums of two squares are exactly 2 and the odd primes congruent ...
Square number 16 as sum of gnomons. In mathematics, a square number or perfect square is an integer that is the square of an integer; [1] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3 2 and can be written as 3 × 3.