# It's prime time for Glenbrook North prime number sleuths

Prime numbers are whole numbers divisible only by 1 and themselves.

Numbers like 5 and 7, Glenbrook North High School computer science and math teacher Steve Goodman tells the layman.

Late in the Cold War, Goodman said, cryptologists used large prime numbers - huge numbers of multiple digits - to send messages.

These days, and now at Glenbrook North, the search for these rarities serves another interest.

"What I like about it is it generates excitement about mathematics. Now it's almost like a treasure-hunting contest," Goodman said. "Professional mathematicians used to be the only ones to search for prime numbers because most of it was done by hand or by similar technology. Now, armed with powerful computers, recreational mathematicians can join the hunt."

He's got two in-house sleuths - Glenbrook North juniors Jack Sloan and David Stolyarov.

Glenbrook North High School students Jack Sloan, left, and David Stolyarov are working with math teacher Steve Goodman on a prime number project. Initially, the boys worked independently at home, but this school year they decided to join forces. Joe Lewnard/jlewnard@dailyherald.com

They're in it, Stolyarov said, "for the fun of the hunt."

"Originally, primes were used for encryption in cyber security, mainly," Sloan said. "They're still used for that to some extent, but ones this big are used for the beauty of mathematics and for finding out things that we don't know. These numbers exist because we know there's an infinite number of primes, we just don't know what they are."

They've identified some whoppers.

Just on Monday, Sloan and Stolyarov used a laptop computer at Glenbrook North, which Goodman and Ryan Manly, Glenbrook High School District 225 technology services manager, arranged for their use.

They found a prime number that is 521,830 digits long: 8139*2^1733467+1. Mathematicians use the asterisk to denote multiplication; the number following the carat is an exponent.

"The larger a number is, the more rare it is for it to be prime, just because of how many possible factors there are that come before it," Stolyarov said.

Monday's discovery eclipses the boys' prior record-setter found with the school computer. On Dec. 9, they came up with a prime number 518,000 digits long: 3133*2^1723044+1.

"It's never really expected. It'll just happen, and it's really exciting," Stolyarov said.

Primes in the hundreds of thousands of digits are dwarfed by one Sloan found working at home, a "mega prime" that is 1,065,431 digits: 134459616^131072+1.

This whole research project runs on software provided by a site called PrimeGrid. With names like Antarctic Crunchers, Team China and Seventeen or Bust, it counts 353,712 members worldwide. They have discovered more than 89,000 large primes and 1,472 mega primes.

The largest known prime number, a Mersenne Prime found outside of the PrimeGrid program, is 24,862,048 digits long, Sloan said.

Glenbrook North High School students David Stolyarov, right, and Jack Sloan are working with math teacher Steve Goodman on a prime number project. They recently found a prime number that is 521,830 digits long. Joe Lewnard/jlewnard@dailyherald.com

There are different types of prime numbers, based on the algorithms used to find them, Sloan said. The boys seek Proth and Fermat primes at school.

Sloan said the mega prime he found at home, a Fermat Prime, is listed at No. 742 on The Prime Pages, a list of the largest 5,000 prime numbers ever discovered. The boys are listed as "Glenbrook North High School."

"It's exciting to have discovered something that is permanently a part of what we know about math," Sloan said.

"Technically, I get the credit for the mega prime I found, but we're under the understanding that this is a team effort," he said.

Initially, the boys worked independently at home. Stolyarov himself logged several primes of hundreds of thousands of digits running PrimeGrid. Friends already, this school year they decided to join forces.

Fittingly, both juniors are heavily invested in music. Sloan, a guitarist and bassist, plays in Glenbrook North's Jazz Ensemble and is part of Spartan Marching Band.

Stolyarov, also on the school's math and Scholastic Bowl teams, is part of the school Chorale and the Ow! a cappella group, is a percussionist with the Glenbrook North wind and jazz ensembles, the Glenbrook Symphony Orchestra and the Chicago Youth Symphony Orchestra. He's a board member for Tri-M (Modern Music Masters), a nationwide honors music society combining service and performance.

Melding music and math, Stolyarov also is participating in a two-year advanced honors research program in which he composes music using topology and geometry.

With that schedule it's fortunate Stolyarov, Sloan and their fellow investigators use computers rather than calculate figures by hand - by "brute force," as Goodman said.

"When you're talking a number with a million digits you're talking a lifetime," Goodman said.

That may be the span Glenbrook North's prime team is looking at.

"There's not really an end goal, I don't think, until I either get bored of it or I don't feel like doing it anymore," Sloan said. "There's always bigger numbers to find. I'll keep looking for them."