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In 1749, Leonhard Euler solved a longstanding open problem in number theory, proving Fermat's 1640 conjecture that any prime number of the form 4 m + 1 can be written as the sum of two squares. This achievement overshadowed an equally impressive calculation that Euler devised at the same time, to test numbers for primality. In this article, we explore Euler's primality test, demonstrating its computational parity with trial division, at least for a class of testable numbers. Additionally, we will see that primality testing was one of Euler's lifelong interests, and was a topic he returned to time and again as an application of his number theory work. [ABSTRACT FROM AUTHOR]

This work describes the contributions of Leonhard Euler (1707-1783), the 18th- century physicist and mathematician, to the fields of articulatory and experimental phonetics. First the authors provide evidence for Euler's role in establishing the St. Petersburg Academy prize of 1780. Next, they consider a short and posthumously published work of Euler, the Meditatio de formatione vocum. It is shown that the Meditatio represents an early attempt to compare vowels in several languages, and includes a two-dimensional classification of vowels which anticipates in many ways the International Phonetic Alphabet vowel chart. [ABSTRACT FROM AUTHOR]