## THE TRUTH BEHIND PRIME NUMBERS by Simon R. Gladdish

# THE TRUTH BEHIND PRIME NUMBERS by SIMON R. GLADDISH

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**Every school pupil knows or should know what a Prime Number is. It is any number which is divisible only by itself and one. The first few primes are: 2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73 etc.**

**I first became interested in Prime Numbers about a decade ago after thoroughly enjoying a book called ‘My Brain is Open: The Mathematical Journeys of Paul Erdos’ by Bruce Schechter. Paul Erdos was a brilliant Hungarian mathematician who seemed to believe that there was something uniquely mysterious and mystical about Prime Numbers. After reading the chapter on Prime Numbers, I remember thinking that if Prime Numbers are an integral part of a rational number system (which they are) then there must be a limit to how mysterious they can be.**

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**My interest in Prime Numbers was reawakened recently by reading Daniel Tammet’s excellent new book ‘Embracing the Wide Sky’. Daniel Tammet is a high-functioning autistic savant who can learn a foreign language in a week and holds the European record for publicly reciting 22,514 decimal places of Pi purely from memory. Like Erdos, Tammet is mesmerised by Prime Numbers. On page 152 he writes ‘Prime Numbers are fascinating to savants and mathematicians alike: they seem to be randomly distributed along the number line, yet are capable of producing beautiful patterns.’ He goes on to say ‘Primes are not only beautiful numbers, they are useful too, in the field of cryptography. For example, whenever you make a purchase over the Internet, the security of the information sent to other computers is ensured by the use of an encryption method known as RSA (the name derives from the initials of its inventors)’.**

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**Talking of names and inventors, I believe that I have unlocked the essential mystery behind Prime Numbers.**

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** ‘THE GLADDISH CONJECTURE OR THEOREM’ goes as follows:**

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** ‘Every Prime Number is an Even Multiple of Three, Plus or Minus One’ or (to say the same thing slightly differently) ‘Every Prime Number (except 2 and 3) is a Multiple of Six, Plus or Minus One.’
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**Examples:**

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**5 = 3 x 2 – 1**

**7 = 3 x 2 + 1**

**11 = 3 x 4 – 1**

**13 = 3 x 4 + 1**

**17 = 3 x 6 – 1**

**19 = 3 x 6 + 1**

**23 = 3 x 8 – 1**

**29 = 3 x 10 – 1**

**31 = 3 x 10 + 1**

**37 = 3 x 12 + 1**

**41 = 3 x 14 – 1**

**43 = 3 x 14 + 1**

**47 = 3 x 16 – 1**

**53 = 3 x 18 – 1**

**59 = 3 x 20 – 1**

**61 = 3 x 20 + 1**

**67 = 3 x 22 + 1**

**71 = 3 x 24 – 1**

**79 = 3 x 26 + 1**

**83 = 3 x 28 – 1**

**89 = 3 x 30 – 1**

**97 = 3 x 32 + 1**

**101=3 x 34 – 1**

**103=3 x 34 + 1**

**107=3 x 36 – 1**

**109=3 x 36 + 1**

**113= 3 x 38 – 1**

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**QED etcetera ad infinitum**

**The ‘Gladdish Conjecture or Theorem’ makes it much easier to predict and prove Prime Numbers. For example, we know that 59 and 61 are Primes but so are 599 and 601. If an alleged ‘Prime Number’ is not a multiple of 6, plus or minus one, then it cannot be a Prime Number.
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**I really believe that I am on to something here and would like to hear from professional mathematicians to see whether or not they agree with me.**

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**Copyright Simon R. Gladdish 2009-03-12**

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