Alec Wilkinson’s New Yorker profile of mathematician Yitang Zhang is a fascinating character sketch and an introduction to the world of pure mathematics.
Along the way, Wilkinson lists some of the wonders and mysteries of prime numbers: “No formula predicts the occurrence of primes—they behave as if they appear randomly. Euclid proved, in 300 B.C., that there is an infinite number of primes. If you imagine a line of all the numbers there are, with ordinary numbers in green and prime numbers in red, there are many red numbers at the beginning of the line: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47 are the primes below fifty. There are twenty-five primes between one and a hundred; 168 between one and a thousand; and 78,498 between one and a million. As the primes get larger, they grow scarcer and the distances between them, the gaps, grow wider. . . . From ‘ Prime Curios! ,’ by Chris Caldwell and G. L. Honaker, Jr., I know that an absolute prime is prime regardless of how its digits are arranged: 199; 919; 991. A beastly prime has 666 in the center. The number 700666007 is a beastly palindromic prime, since it reads the same forward and backward. A circular prime is prime through all its cycles or formulations: 1193, 1931, 9311, 3119. There are Cuban primes, Cullen primes, and curved-digit primes, which have only curved numerals—0, 6, 8, and 9.”
It’s enough to turn the unsuspecting reader into a passionate Pythagorean.
Peter Leithart
Peter J. Leithart is President of Theopolis Institute. He is the author of numerous books on theology, literature, and culture, including Theopolitan, Defending Constantine, and Baptized Body.
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