Further tabulation of the Erdös-Selfridge function
نویسندگان
چکیده
For a positive integer k, the Erdös-Selfridge function is the least integer g(k) > k + 1 such that all prime factors of (g(k) k ) exceed k. This paper describes a rapid method of tabulating g(k) using VLSI based sieving hardware. We investigate the number of admissible residues for each modulus in the underlying sieving problem and relate this number to the size of g(k). A table of values of g(k) for 135 ≤ k ≤ 200 is provided.
منابع مشابه
A Refinement of the Function g(x) on Grimm’s Conjecture
In this paper, we refine the function g(x) on Grimm’s conjecture and obtain an analogical result of Erdös and Selfridge without using Hall’s theorem.
متن کاملOn a Problem of P . Erdös and S. Stein
is called a covering system if every integer satisfies at least one of the congruences (1) . An old conjecture of P . Erdös states that for every integer a there is a covering system with n l = c. Selfridge and others settled this question for c < 8 . The general case is still unsettled and seems difficult . A system (1) is called disjoint if every integer satisfies at most one of the congruenc...
متن کاملIntegers Not of The
Let N = {0, 1, 2, · · · } and P denote the set of (positive) primes. In 1950 van der Corput [Co] showed that those positive odd integers not representable in the form 2 + p (where a ∈ N and p ∈ P), form a subset of Z = {1, 2, 3, · · · } with positive lower asymptotic density. By means of cover of the ring Z of integers, P. Erdös [E] constructed a residue class of odd numbers which contains no i...
متن کاملThe Pseudoprimes to 25 • 109
The odd composite n < 25 • 10 such that 2n_1 = 1 (mod n) have been determined and their distribution tabulated. We investigate the properties of three special types of pseudoprimes: Euler pseudoprimes, strong pseudoprimes, and Carmichael numbers. The theoretical upper bound and the heuristic lower bound due to Erdös for the counting function of the Carmichael numbers are both sharpened. Several...
متن کاملThe Product of Consecutive Integers Is Never a Power
has no solution in integers with k >_ 2, 1 >_ 2 and n >_ 0 . (These restrictions on k, 1 and n will be implicit throughout this paper .) The early literature on this subject can be found in Dickson's history and the somewhat later literature in the paper of Obláth [5] . Rigge [6], and a few months later Erdös [1], proved the conjecture for 1 = 2 . Later these two authors [1] proved that for fix...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 66 شماره
صفحات -
تاریخ انتشار 1997