Francis J. Conlan’s book explores how to classify numbers as prime or composite. It focuses on natural numbers, especially odd ones ending in 1, 3, 7, or 9. The book introduces a method to determine if a number is composite by factoring and suggests a new approach to identifying primes.
Francis J. Conlan was born in Bristol, Connecticut. He has a strong academic and professional background, including 11 years of undergraduate study. During this time, he earned several degrees, including a BA in Mathematics, Physics, and Microbiology, as well as BS degrees in Chemistry and Business Finance. He then spent 20 years in graduate studies, earning a PhD in Theoretical Chemistry, an MA in Mathematics, and two MS degrees in Statistics and Applied Mathematics.
From 1988 to 1995, Conlan was an Assistant Professor of Applied Mathematics at Santa Clara University, where he developed and taught courses such as Ordinary Differential Equations,
“The Arithmetical Minimum” by Francis J. Conlan explains the classification of numbers as prime or composite, focusing on natural numbers and their subsets. It divides natural numbers into even and odd categories and further into prime and composite groups, refining these to highlight useful subsets. The book covers the properties of even and odd numbers, including the roles of 0 as the additive identity and 1 as the multiplicative identity. It defines prime and composite numbers and explores methods for factoring them, showing how to determine if a number is composite by breaking it down into smaller natural number divisors. The text emphasizes the significance of odd numbers ending in 1, 3, 7, or 9 and introduces the idea that a number’s position can help identify whether it is prime or composite. This offers a fresh perspective on Gauss’s problem of distinguishing prime numbers from composite ones.
In this first chapter we introduce the reader to two types of numbers that we’ll attempt to characterize as being prime or composite. As J. C. F. Gauss1 proposed in the early nineteenth century,
The primary objective of this investigation is the “problem of distinguishing prime numbers from composite numbers…”. In Chapter 1 we left off merely looking at the digits making up a typical odd number’s value. We decided that in order to pursue Gauss’s important objective we would need to limit our investigation to odd numbers larger than 3 with 1, 3, 7, or 9 in their unit’s place.
Since our investigations are based on simple arithmetic we uncover in this chapter an important result that appeared in a correspondence between two men in the 18th century. It uses very simple operations producing profound consequences.
To obtain any (and all) composite odd natural numbers, just multiply them all together, in pairs. Referring to the formula from Equation (1.3) above, k and m will denote any two arbitrary odd number locations and we let l stand for the location of their product.
“A must-read for anyone interested in mathematics!”
John Roberts
“This book gave me a fresh perspective on how numbers are classified. Francis J. Conlan explains the properties of numbers in a way that is easy to understand, even for those who are not math experts. The discussions on factoring and prime numbers are very helpful.”
Daniel Harris
“The Arithmetical Minimum” helped me see numbers in a new way. The book explains how to determine if a number is prime or composite with great clarity. The approach to Gauss’s problem is very interesting, and the examples made it easy to follow. A fantastic read for math lovers!”
Lauren Hall
“This book is a valuable resource for students and teachers alike.”
Matthew Scott
“Francis J. Conlan has written a wonderful book that simplifies the study of numbers. “The Arithmetical Minimum” explains how to identify prime and composite numbers in a unique way. The book’s insights into number properties and factoring methods are both useful and engaging. A great addition to any math library!”
Ashley White
This book helps readers understand numbers, especially primes and composites. It explains even and odd numbers, factoring, and how to identify primes. With a fresh approach to Gauss’s problem, it offers simple methods to explore number properties in new ways.
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