How To Use Rice And A Chessboard To Find Primes !

Legend has it that Chess was invented in India by a mathematician. The King was so grateful to the mathematician that he asked him to name any prize as a reward. The inventor thought for a minute, then asked for 1 grain of rice to be placed on the first square of the chessboard, 2 on the second, 4 on the third, 8 on the fourth, and so on, so that each square got twice as many grains of rice as were on the previous square.

The King readily agreed, astonished that the mathematician wanted so little – but he was in for a shock. When he began to place rice on the board, the first few grains could hardly be seen. But by the time he’d got to the 16th square, he was already needing another kilogram of rice. By the 20th square, his servants had to bring in a wheelbarrow full. He never reached the 64th and last square on the board. By that point, the total number of grains of rice on the board would’ve been a staggering ….

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Mysterious Prime Series

Here are few amazing prime numbers, but it discontinues when eights 3’s are joined before 1 :

31
331
3331
33331
333331
3333331
33333331

The next number 333333331 is not a prime number. Where it is multiplied by 17 x 19607843 = 333333331.

The real mystery lies within 30, 300, 3000, 30000, etc…. or with 3*(10^n).
When these numbers are added to primes 1, 31, 331, 3331, etc… respectively it always results in a prime , however this tradition discontinues with 333333331.

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The Fool-proof Prime Test

It’s been a long time since mathematicians have discovered tests (  or equations as you like it ) for searching and exploring new primes…

But most of them are faulty and are not perpetually flawless

However, with the flow of advancements, mathematicians have discovered a new fool-proof test for prime which always works and that’s the reason I just love it , And this one is particularly flawless – ‘perpetually’ … And Here’s the mind blowing , short & smart equation :

(x-1)^p  –  ( x^p – 1)

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Little Fermat Theorm

This Theorem consists of a trick that I would like to share …

Let p be any prime number greater than n (which may be any number ) . You may carry out the following calculation to view the result yourself !

  1.  Raise n to the power of p, to obtain x
  2.  Divide –  x / p , Let the remainder of this calculation be q
  3.  interestingly q = n….

Example –  

  • p = 5 , n = 4
  • n^p = 4^5 = 1024
  • x = 1024,    So =>   1024 / 5(p) , where the remainder is 4

Therefore , n = q (4) ….

Shamoil Khomosi
Admin @ Fantastic Number