UIL NS and Mathematics Special Topics Session
Special session for
Not the Ordinary Types of Numbers
(Part 1)
UIL NS and Mathematics Special Topics Session
Larry White
Box 25
Millersview, Tx 76862
325-483-5446
UIL State NS & Mathematics Contest Director
Be sure to ...
Ø sign in;
Ø clean up your area when
you leave;
Ø and
“HAVE A GREAT DAY!”
UIL NS and Mathematics Special Topics Session
UIL Number Sense and Mathematics
Constitution and Contest Rules (C&CR)
??? Any rules need discussing or clarified ???
UIL NS and Mathematics Special Topics Session
No special topics this year
Items of emphasis will include:
Functions Circles
Platonic Solids Patterns Fibonacci
UIL NS and Mathematics Special Topics Session
Two new mathematicians
Franciscus Vieta
Marin Mersenne UIL NS and Mathematics Special Topics Session
Two new special types of numbers
Germain Primes
Mersenne Primes UIL NS and Mathematics Special Topics Session
Not the Ordinary Types of Numbers
(Part 1)
Special Primes
UIL NS and Mathematics Special Topics Session
Germain Primes These are Germain Primes:
3, 11, 29, …
These are not Germain Primes:
7, 13, 31, …
UIL NS and Mathematics Special Topics Session
Germain Primes
If P is prime and 2P + 1 is prime, then P is a Germain prime.
2 ? 41 ? 37 ?
UIL NS and Mathematics Special Topics Session
Mersenne Primes These are Mersenne Primes:
2, 3, 5, …
These are not Mersenne Primes:
11, 23, 31, …
UIL NS and Mathematics Special Topics Session
Mersenne Primes P If P is prime and 2 -1 is prime, then P is a Mersenne prime.
7 ? 13 ? 29 ?
UIL NS and Mathematics Special Topics Session
Mersenne Primes titanic primes --- Mersenne primes with more than 1000 digits
gigantic primes --- Mersenne primes with more than 10,000 digits
megaprimes --- Mersenne primes with more than 1,000,000 digits
UIL NS and Mathematics Special Topics Session
Mersenne Primes
Note: The ten largest known Mersenne primes are the biggest prime numbers ever identified thus far.
Note: The largest Mersenne primes is 2 57,885,161 – 1
It was discovered in 2013 and has more than 17,000,000 digits.
UIL NS and Mathematics Special Topics Session
Pythagorean Primes These are Pythagorean Primes:
5, 13, 41, …
These are not Pythagorean Primes:
3, 11, 23, …
UIL NS and Mathematics Special Topics Session
Pythagorean Primes
If N is a natural number and
P = 4N + 1 is prime, then then P is a Pythagorean prime
2 ? 7 ? 31 ?
UIL NS and Mathematics Special Topics Session
Factorial Primes These are Factorial Primes:
3, 5, 7, …
These are not Factorial Primes:
11, 13, 17, …
UIL NS and Mathematics Special Topics Session
Factorial Primes
If N is a natural number and
P = N! + 1 or P = N! - 1is prime, then then P is a Factorial prime.
2 ? 17 ? 23 ?
UIL NS and Mathematics Special Topics Session
Not the Ordinary Types of Numbers (Part 1)
There are some real interesting things to learn about these special primes as well as other types of primes. Do some investigating and enjoy.
HAVE A
GREAT DAY!