20 research outputs found
Verifying Sierpi\'nski and Riesel Numbers in ACL2
Full text linkA Sierpinski number is an odd positive integer, k, such that no positive
integer of the form k * 2^n + 1 is prime. Similar to a Sierpinski number, a
Riesel number is an odd positive integer, k, such that no positive integer of
the form k * 2^n + 1 is prime. A cover for such a k is a finite list of
positive integers such that each integer j of the appropriate form has a
factor, d, in the cover, with 1 < d < j. Given a k and its cover, ACL2 is used
to systematically verify that each integer of the given form has a non-trivial
factor in the cover.Comment: In Proceedings ACL2 2011, arXiv:1110.447
The mathematics devotional: Celebrating the wisdom and beauty of mathematics
No full textNew York388 p.: bibl.; 20 c
Stars of heaven
No full textDo a little armchair space travel, rub elbows with alien life forms, and stretch your mind to the furthest corners of our uncharted universe. With this astonishing guidebook, you don't have to be an astronomer to explore the mysteries of stars and their profound meaning for human existence. Clifford A. Pickover tackles a range of topics from stellar evolution to the fundamental reasons why the universe permits life to flourish. He alternates sections that explain the mysteries of the cosmos with sections that dramatize mind-expanding concepts through a fictional dialog between futuristic huma
The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions
No full textHumanity's love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained fifteen dots, as did the columns and diagonals. When he added any two cells opposite along a line through the center square, like 2
