منابع مشابه
Three new factors of Fermat numbers
We report the discovery of a new factor for each of the Fermat numbers F13, F15, F16. These new factors have 27, 33 and 27 decimal digits respectively. Each factor was found by the elliptic curve method. After division by the new factors and previously known factors, the remaining cofactors are seen to be composite numbers with 2391, 9808 and 19694 decimal digits respectively.
متن کاملTwo New Factors of Fermat Numbers
We report the discovery of new 27-decimal digit factors of the thirteenth and sixteenth Fermat numbers. Each of the new factors was found by the elliptic curve method. After division by the new factors and other known factors, the quotients are seen to be composite numbers with 2391 and 19694 decimal digits respectively.
متن کاملFactors of generalized Fermat numbers
A search for prime factors of the generalized Fermat numbers Fn(a, b) = a2 n + b2 n has been carried out for all pairs (a, b) with a, b ≤ 12 and GCD(a, b) = 1. The search limit k on the factors, which all have the form p = k · 2m + 1, was k = 109 for m ≤ 100 and k = 3 · 106 for 101 ≤ m ≤ 1000. Many larger primes of this form have also been tried as factors of Fn(a, b). Several thousand new fact...
متن کاملTable errata 2 to "Factors of generalized Fermat numbers"
We note that three factors are missing from Table 1 in Factors of generalized Fermat numbers by A. Björn and H. Riesel published in Math. Comp. 67 (1998), 441–446. In Table 1 in Björn–Riesel [2] there are unfortunately three factors missing. Fougeron [3] discovered that 31246291 · 2 + 1 ∣ ∣ 11 51 + 1 and 33797295 · 2 + 1 ∣ ∣ 10 62 + 3 62 . He also verified that no other factors are missing for ...
متن کاملMersenne and Fermat Numbers
The first seventeen even perfect numbers are therefore obtained by substituting these values of ra in the expression 2n_1(2n —1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 2127 —1, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime. More details on the history of the Mersenne numbers may be found in ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1978-0472664-4