Constructing Carmichael numbers through improved subset-product algorithms
نویسندگان
چکیده
We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two new algorithms for the subset product problem that exploit the non-uniform distribution of primes p with the property that p − 1 divides a highly composite Λ.
منابع مشابه
A new algorithm for constructing large Carmichael numbers
We describe an algorithm for constructing Carmichael numbers N with a large number of prime factors p1, p2, . . . , pk. This algorithm starts with a given number Λ = lcm(p1 − 1, p2 − 1, . . . , pk − 1), representing the value of the Carmichael function λ(N). We found Carmichael numbers with up to 1101518 factors.
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ورودعنوان ژورنال:
- Math. Comput.
دوره 83 شماره
صفحات -
تاریخ انتشار 2014