Odd Perfect Numbers: A Search Procedure, and a New Lower Bound of 10 36

1973 ◽  
Vol 27 (124) ◽  
pp. 1004
Author(s):  
D. S. ◽  
Bryant Tuckerman
Keyword(s):  
Lower Bound ◽  
Search Procedure ◽  
Perfect Numbers

A lower bound for \tau(n) of any k-perfect numbers

2015 ◽  
Vol 4 ◽  
pp. 99-103
Author(s):  
Keneth Adrian P. Dagal
Keyword(s):  
Lower Bound ◽  
Perfect Numbers

scholarly journals On the Ramsey Number $R(4,6)$

10.37236/2102 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Fixed Point ◽  
Automorphism Group ◽  
Lower Bound ◽  
Heuristic Search ◽  
Ramsey Number ◽  
Complete Graphs ◽  
Search Procedure ◽  
Edge Colorings

The lower bound for the classical Ramsey number $R(4,6)$ is improved from 35 to 36. The author has found 37 new edge colorings of $K_{35}$ that have no complete graphs of order 4 in the first color, and no complete graphs of order 6 in the second color. The most symmetric of the colorings has an automorphism group of order 4, with one fixed point, and is presented in detail. The colorings were found using a heuristic search procedure.

scholarly journals A new lower bound for odd perfect numbers

1989 ◽  
Vol 53 (187) ◽  
pp. 431 ◽  
Author(s):  
Richard P. Brent ◽  
Graeme L. Cohen
Keyword(s):  
Lower Bound ◽  
Perfect Numbers

Supplement to A New Lower Bound for Odd Perfect Numbers

1989 ◽  
Vol 53 (187) ◽  
pp. S7
Author(s):  
Richard P. Brent ◽  
Graeme L. Cohen
Keyword(s):  
Lower Bound ◽  
Perfect Numbers
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