Everyone wants to believe their online communications and transactions are secure.
The way companies secure them is though cryptographic algorithms, which use really large prime numbers as their encryption keys.
But there are some numbers that mirror primes.
“And that’s problematic, because these numbers, which are called Carmichael numbers, show up as primes even though they’re not actually prime,” said Bloomington High School South senior Daniel Larsen. “And that leads to weaker encryption.”
So, Larsen went to work on understanding Carmichael numbers based on a 19th century finding on the large gaps between consecutive primes. And it led to a possible breakthrough in mathematics.
“What it says in particular is that for every X, there exists a prime between X and 2X,” Larsen said. “And I showed that the analogous result is true for Carmichael numbers instead of primes.”
And that should make it easier to filter Carmichael numbers out of the equation - and make your transactions and communications more secure.
Last week, Larsen presented his work at the prestigious Regeneron Science Talent Search in Washington, D.C. And out of the 40 high school seniors competing in the week-long competition, Larsen placed fourth and earned a $100,000 scholarship. The talent search awarded $1.8 million in scholarship money this year.
“I’m thankful that it was in person, the last few years have been virtual,” Larsen said. “It was just great meeting all these people and being in D.C.”
Just making it to the nation’s oldest science and math competition was an accomplishment. More than 1,800 seniors entered the talent search this year. Former competitors have gone on to win 13 Noble Prizes, 11 National Medals of Science, 22 MacArthur Foundation Fellowships and are leaders in the industry.
“I think it’s not so surprising that a lot of them became very important scientists,” Larsen said. “But, of course, it is still cool seeing yourself in the same competition that all these great scientists were in.”
Larsen has been accepted at the Massachusetts Institute of Technology but is waiting to hear from other universities before making his final decision on where to go to college.
