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The number 28 depicted as 28 balls arranged in a triangular pattern with the number of layers of 7 28 as the sum of four nonzero squares. Twenty-eight is a composite number and the second perfect number as it is the sum of its proper divisors: 1 + 2 + 4 + 7 + 14 = 28 {\displaystyle 1+2+4+7+14=28} .
For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28. The first four perfect numbers are 6, 28, 496 and 8128. [1] The sum of proper divisors of a number is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum.
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. The largest 18 of these have been discovered by the distributed computing project Great Internet Mersenne Prime Search , or GIMPS; their discoverers are listed as "GIMPS / name ", where the name ...
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 next number not yet crossed out in the list after 5 is 7; the next step would be to cross out every 7th number in the list after 7, but they are all already crossed out at this point, as these numbers (14, 21, 28) are also multiples of smaller primes because 7 × 7 is greater than 30.
The hot, dry and windy conditions that preceded the Southern California fires were about 35% more likely because of climate change, according to a new report.
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If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem.