Amazing Facts on Prime Numbers

1. Amazing Facts on Prime Numbers

2. What are Prime Numbers? • A prime number is a number which can be divided without a remainder only by itself and by 1. For example: 17 can be only divided by 17 and 1.

3. Some Facts on Prime Numbers • The only even prime number is 2. All other even numbers can be divided by 2. • If the sum of a number’s digits is a multiple of 3, that number is divided by 3. • No prime number greater than 5 ends in 5. Any number greater than 5 that ends in 5 can be divided by 5. • Zero and 1 are not considered prime numbers. • Except for 0 and 1 a number is either a prime or a composite number.

4. Table of Prime Numbers up to 1000

5. Amazing Facts on Prime Numbers

6. Prime Spirals In 1963, the mathematician Stanislaw Ulam noticed an odd pattern while doodling in his notebook during a presentation: When integers are written in a spiral, prime numbers always seem to fall along diagonal lines. This in itself wasn't so surprising, because all prime numbers except for the number 2 are odd, and diagonal lines in integer spirals are alternately odd and even. Much more startling was the tendency of prime numbers to lie on some diagonals more than others — and this happens regardless of whether you start with 1 in the middle, or any other number.

7. Fun Facts • Prime numbers are often used in cryptography or security for technology and the internet. • The number 1 used to be considered a prime, but it generally isn't any more. • The largest prime number known has around 13 million digits! • The Greek mathematician Euclid studied prime numbers in 300BC. • The number 379009 is a prime number. It's also Google if you type into a calculator and look at it upside down!

8. Fun Facts • Here is a interesting sequence of prime numbers in which all the digits involved have circles in them: • 6089 • 60899 • 608999 • 6089999 • 60899999 • 608999999

10. Prime triplets • In 1988 Dubner searched for triplets in arithmetic progression with the first term equal to 3, like (3, 5, 7), (3, 7, 11), (3, 11, 19), (3, 23, 43), etc. • In particular he searched for triplets of the form (3, a + 1,  2*a –1). Here are three of his biggest triplets:

11. Heinz Rectangles • A Heinz Rectangle of prime numbers is where the rows and columns are addition of primes, and the sums of the rows must be a prime number too. Each number following the previous prime must be the next prime number. The first prime on second row is the second number on the first row (or the first number on second column.)

12. Heinz rectangles • The simplest 3x3 rectangle: 5+7+11=23 7+11+13=31 11+13+17=41 •  A4×5 rectangle 5+7+11+13+17=53 7+11+13+17+19=67 11+13+17+19+23=83 13+17+19+23+29=101

13. Growing primes

14. Left Truncatable Primes • 357686312646216567629137 is the largest right truncatable prime such that all of the substrings of the original prime are also prime numbers. • 357686312646216567629137 • 57686312646216567629137 • 7686312646216567629137 • 686312646216567629137 • 86312646216567629137 • 6312646216567629137 • 312646216567629137 • 12646216567629137 • 2646216567629137........ • 9137 • 137 • 37 • 7

15. Right Truncatable Primes • 73939133 is a prime & the largest ever possible prime such that all of the substrings of the original prime are also prime numbers. • 739391337393913739391739397393739737

16. Prime Number Trick • 1.Pick any prime number greater than 3.2. Square it.3. Add 14.4. Divide by 12. • Without knowing which prime number you picked, I can tell you: There will be a remainder of 3.

17. Thank you

18. Made by: Vedika gupta: 2548 Narendrayadav: 2547 Sanyam: 2549