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Thursday, April 08, 2021

Mathematicians Discovered a New Kind of Prime Number | Science - Popular Mechanics

  • Digitally delicate prime numbers become composite with this one weird trick.
  • Math researchers proved these primes exist using the bucket proof method.
  • There are no known examples so far, but mathematicians are hopeful.


In new research, mathematicians have revealed a new category of “digitally delicate” prime numbers. These infinitely long primes turn back to composites faster than Cinderella at midnight with a change of any individual digit, as Caroline Delbert, writer, book editor, researcher, and avid reader reports.

 Photo: amtitusGetty Images

Digitally delicate primes have infinite digits, and changing any digit to any other value bears a composite number outcome instead. To use a more bite-size example, consider 101, which is a prime. Change the digits to 201, 102, or 111, and you have values that are divisible by 3 and therefore compound numbers.

This idea is decades old, so what’s new?...

South Carolina math professor Michael Filaseta and former graduate student Jeremiah Southwick worked together on the widely digitally delicate number research, publishing their findings in Mathematics of Computation and arXiv. Even without specific examples, they proved the numbers exist in base 10 (meaning numbers that use our 0-9 counting system; compare with binary, base 2, with just 0 and 1) and that there are infinitely many.

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Source: Popular Mechanics