October 28 - Happy Birthday, Landon Curt Noll

nPosted October 28, 2018

Key Points

nBorn on this date in California, in 1960, Landon Curt Noll was able to make a Wikipedia-worthy contribution while still in high school!!

Noll was just 18 years old, and still enrolled in high school but also attending university classes, when he broke a record for discovering the largest known prime number. That makes him the youngest person ever to break that record.

nActually, Noll has held or co-held the largest-known-prime record three times.

nLest you think that there is no use to prime numbers, and that Noll has wasted his life, he has also served his community in local politics, has made contributions to astronomy, and has furthered computer science. He has traveled to Antarctica multiple times to search for meteorites.

Here is a photo taken in Antarctica on one of Noll’s travels.

nBut let’s get back to prime numbers…

nI bet you remember that a prime number is a whole number greater than 1 whose ONLY factors are 1 and itself. In other words, 2 is prime because the only ways we can multiply two whole numbers and get the answer “2” are:

n1 times 2 – and of course the reverse, 2 times 1

nAnd that means that 2 has only two factors: 1 and itself.

nHere is an example of a number that is NOT prime:

n12 has several factors: 1, 2, 3, 4, 6, and 12

n1 times 12 = 12

n2 times 6 = 12

n3 times 4 = 12

nThe first few prime numbers are easy for all of us to figure out:

n2, 3, 5, 7, 11…

nBut eventually we get to numbers we have to ponder a bit. Obviously, no even number other than 2 is prime, because it would have 2 as a factor, as well as 1 and itself. So, if you are ever asked if a number is a prime number, you can immediately answer “nope” if the number ends with 0, 2, 4, 6, or 8.

nBut many odd numbers have factors other than 1 and themselves.

n9 = 3 times 3

n15 = 3 and 5

n21 = 3 times 7

n27 = 3 times 9

nYou can make a pretty good start at figuring out larger prime numbers by testing to see if the first few odd prime numbers can be evenly divided into that number. To test 31, for example, divide it by 3, 5, 7, and 11. Each of these divisions turn out to be include messy decimals – so we know that 31 is a prime. If you do the same for other odd numbers such as 33 and 35, you quickly find factors other than 1 and themselves.

Prime numbers get more rare as numbers get larger.

nHere are a few large prime numbers:

n8,191

n6,700,417

n20,988,936,657,440,586,486,151,264,256,610,222,593,863,921

nThat last one is really large! It has 44 digits! It was discovered in 1951 by Aime Ferrier, who used just a mechanical calculator. It is the largest prime ever found before the use of electronic computers (it was discovered in 1951, so there were electronic computers, at that point, but nobody had yet used them to find a prime number).

nSo, I was saying HOW LARGE Ferrier’s prime is, with 44 digits, but Noll’s first prime has 6,533 digits!!!!

nI mean, yi-yi-yi!

nOh, and by the way, that crack I made above about prime numbers being useless – that’s so, so, so, so, SO not true.

Large prime numbers are used for computer cryptography. Creating codes that others cannot crack is not just a great way to stump enemies during a war, it’s a great way of keeping your identity, money, and private information safe.

nWe use computer encryption every single day – buying things online, logging into your bank from your phone, etc. – and that means that we use and rely on prime numbers every day.

nThere are loads of other uses of prime numbers:

Primes can be used to encode two-dimensional pictured information. If you create a picture made up of black-or-white (on-or-off) squares in a grid that has a number of squares that is the product of two prime numbers, then another intelligent being (maybe an alien?) could possibly decode the information by arranging the picture only two ways, and seeing which way works as sensible picture.

nThis idea was proposed by astronomers Frank Drake and Carl Sagan to communicate with possible alien intelligences, somewhere in the universe, and one message encoded in this way has been sent out into the cosmos!

Prime numbers can be used when creating electronic games and anything else that need random numbers.

nPrime numbers are used in other ways in coding (that is, computer programming), such as error correcting code and hashes.

nPrime numbers can be used to make animation more lifelike, by having, say, blades of grass bend at different times.

nPrime numbers help in the development of machine tools, because it’s important to avoid harmonics that will make too much vibration – and will make the tools wear out much faster.

In the olden days of microwave ovens, no metal could be placed in the microwave – there’d be sparks and fires and what not! But nowadays there are some metal racks and turntables designed to be in microwave ovens – and that’s because the metal is designed – using prime numbers – to be tuned to the cavity of the oven. As long as the rack is used properly and doesn’t touch the walls or floor of the microwave, there will be no arc, no spark, no fire!

nThere are probably other real-world applications of prime numbers. But I think you can see my point – they’re not just cool, they’re crucial!