Approximately Counting Semismooth Integers

Eric Bach; Jonathan P Sorenson

doi:10.1145/2465506.2465933

Approximately Counting Semismooth Integers

Butler University

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Original language	American English
Title of host publication	Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation (ISSAC 2013)
DOIs	https://doi.org/10.1145/2465506.2465933
State	Published - Jun 2013

Disciplines

Theory and Algorithms
Number Theory

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10.1145/2465506.2465933License: Unspecified

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title = "Approximately Counting Semismooth Integers",

author = "Eric Bach and Sorenson, {Jonathan P}",

note = "ABSTRACT An integer n is ( y,z)-semismooth if n=pm where m is an integer with all prime divisors ≥ y and p is 1 or a prime ≥ z. Large quantities of semismooth integers are utilized in modern integer factoring algorithms, such as the number field sieve, that incorporate the so-called large prime variant.",

year = "2013",

month = jun,

doi = "10.1145/2465506.2465933",

language = "American English",

booktitle = "Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation (ISSAC 2013)",

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TY - CHAP

T1 - Approximately Counting Semismooth Integers

AU - Bach, Eric

AU - Sorenson, Jonathan P

N1 - ABSTRACT An integer n is ( y,z)-semismooth if n=pm where m is an integer with all prime divisors ≥ y and p is 1 or a prime ≥ z. Large quantities of semismooth integers are utilized in modern integer factoring algorithms, such as the number field sieve, that incorporate the so-called large prime variant.

PY - 2013/6

Y1 - 2013/6

UR - https://doi.org/10.1145/2465506.2465933

U2 - 10.1145/2465506.2465933

DO - 10.1145/2465506.2465933

M3 - Chapter

BT - Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation (ISSAC 2013)

ER -

Approximately Counting Semismooth Integers

Disciplines

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