The prime factorization method can be applied by adding a new prime number for every additional layer of infinity ( 2 ^ s 3 ^ c 5 ^ f, with f the ferry ).
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It can be represented by the exponent vector ( 3, 2, 0, 1 ), which gives the exponents of 2, 3, 5, and 7 in the prime factorization.
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You can figure out the totient from the prime factorization of n + 1 and ( just guessing ) you have higher chances of a match when n + 1 is made of small factors.
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However, it is possible to trick a verifier into accepting a composite number by giving it a " prime factorization " of " n " & minus; 1 that includes composite numbers.
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It considers the connection between perfect numbers and Mersenne primes ( known as the Euclid Euler theorem ), the prime factorizations ), and the Euclidean algorithm for finding the greatest common divisor of two numbers.
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For instance the statement " an integer's prime factorization is unique " up to ordering " ", means that the prime factorization is unique if we disregard the order of the factors.
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For instance the statement " an integer's prime factorization is unique " up to ordering " ", means that the prime factorization is unique if we disregard the order of the factors.
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Any function in the library can be executed from a regular BASIC program by using GOTO " LIB0 : NNNN " where NNNN is the function number ( e . g . 5010 for prime factorization ).
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An "'equidigital number "'is a number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1.
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Iteratively dividing by the " p " factors shows that each " p " has an equal counterpart " q "; the two prime factorizations are identical except for their order.
