Mathematicians Discover New Kind of Prime Number

Digitally delicate primes turn composite with a single digit change.

Published on Feb. 18, 2026

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Researchers at the University of South Carolina have proven the existence of a new category of 'digitally delicate' prime numbers that become composite numbers when any single digit is changed. These infinitely long primes, known as 'widely digitally delicate primes,' have no known real-world examples so far, but the mathematicians believe there are infinitely many of them.

Why it matters

This discovery expands our understanding of the properties and limits of prime numbers, which are fundamental building blocks of mathematics. While these 'digitally delicate' primes have no immediate practical applications, the research provides new insights into the complex and often counterintuitive nature of prime numbers.

The details

Digitally delicate primes are defined as infinitely long prime numbers that become composite (divisible) numbers when any single digit is changed. The researchers focused on a specific subset called 'widely digitally delicate primes,' which have additional leading zeros that don't change the original prime value but make the number more sensitive to digit changes. For example, the prime number 101 becomes composite when changed to 201, 102, or 111, but the 'widely digitally delicate' prime 000101 becomes composite when any of the leading zeros are changed.

  • The research was published in February 2026 in the journal Mathematics of Computation.

The players

Michael Filaseta

A math professor at the University of South Carolina who co-authored the research on widely digitally delicate primes.

Jeremiah Southwick

A former graduate student at the University of South Carolina who co-authored the research on widely digitally delicate primes with Professor Filaseta.

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What they’re saying

“The situation involving widely digitally delicate primes is more complicated, of course. You'll need a lot more buckets, something on the order of 1,025,000, and in one of those buckets every prime number is guaranteed to become composite if any of its digits, including its leading zeros, is increased.”

— Steve Nadis (Quanta)

What’s next

Mathematicians plan to continue exploring the properties and potential applications of digitally delicate primes, including searching for real-world examples and investigating other specialized subsets of these unique prime numbers.

The takeaway

This discovery of 'digitally delicate' primes that become composite with a single digit change highlights the complex and often counterintuitive nature of prime numbers, which are fundamental to mathematics. While these primes have no immediate practical uses, the research expands our understanding of the limits and behaviors of these essential mathematical building blocks.