The allure of prime numbers has long captivated mathematicians, with their history tracing back to ancient Greece. Recently, Jeremiah Bartz, an associate professor of Mathematics at the University of North Dakota (UND), highlighted this fascination in an article for The Conversation. The piece discusses prime numbers’ historical significance and their mathematical intrigue.
Bartz’s article has garnered significant attention, republished by 23 media outlets and read over 37,000 times globally. The Conversation is known for its “explanatory journalism” by university scholars, providing free content for republication.
Prime numbers are defined as whole numbers greater than one that have no divisors other than one and themselves. Peter S. Rudman notes that Greek mathematicians were among the first to grasp this concept around 500 B.C.E., with Euclid later proving there are infinitely many primes.
During the Middle Ages, Arab mathematicians advanced prime number theory further. Kamal al-Din al-Farisi developed the fundamental theorem of arithmetic, emphasizing primes as essential building blocks for constructing any positive integer.
In 1202, Leonardo Fibonacci introduced a type of prime number now called Mersenne primes—numbers of the form (2p – 1) where p is also prime. Despite early conjectures about these numbers always being prime when p is prime, Hudalricus Regius disproved this in 1536 by showing that (211 – 1) equals 2047—a non-prime number.
The search for large primes intensified with Édouard Lucas’s development of a testing algorithm in 1878 and subsequent improvements by Derrick Henry Lehmer in 1930. Raphael M. Robinson identified five new Mersenne primes using computers in the 1950s, marking a significant advancement.
George Woltman’s Great Internet Mersenne Prime Search (GIMPS), launched in 1996, has played a pivotal role in discovering large primes through collaborative computing efforts. GIMPS recently discovered the largest known prime—(2136,279,841 – 1)—found by Luke Durant using cloud-based computing across multiple countries.
The Electronic Frontier Foundation incentivizes these discoveries with cash prizes for identifying large primes. Enthusiasts continue striving to find record-breaking numbers such as the first verified 100 million-digit and billion-digit primes.
