Amazing Facts on Prime Numbers

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.

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.

Table of Prime Numbers up to 1000   2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997

Amazing Facts on Prime Numbers

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.

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!

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

Here are few amazing prime numbers, these prime numbers were proved by the XVIIIthcentury. 31 331 3331 33331 333331 3333331 33333331 The next number 333333331 is not a prime number. Whereas it is multiplied by 17 x 19607843 = 333333331.

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: First prime Second prime Third prime Digits 3 415587*10^800+1 831174*10^800 - 1 806 235398*10^1000+1 470796*10^1000 – 1 1006 87114*10^1100+1 174228*10^1100 – 1 1106

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.)

Heinz rectangles A 4×5 rectangle The simplest 3x3 rectangle: 5+7+11=23 7+11+13=31 11+13+17=41  A 4×5 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

Growing primes

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

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. 73939133 7393913 739391 73939 7393 739 73 7

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.

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