Saturday, 14 May 2016

Prime Number Generator: Chapter 1 - the Challenge

My next few posts will constitute a “sub series” about my Prime Number Generator. This series is related to a far broader and more important series on “Encryption – breaking the myth”.
In the last two posts, I have endeavored to present empirical data. Pragmatically one may easily recognize that:
1. Encryption is being used to secure data.
2. Breaches have occurred.
3. Readable data was acquired by those who don’t have a right to the data.
4. Conclusion: Encryption is failing to properly secure data.

Chapter 1 – the Challenge

The year is 1977. Location: Windsor Ontario, Canada. Yes, once upon a time, Ontario had 5 years of high school. Juniors are in grades 9 and 10. Seniors are grouped into grades 11, 12 & 13.

Happily, there were three math courses offered in Grade 13, and this lover of math signed up for all three.

Mr. Taylor taught Algebra. He was introducing “Prime numbers”. Optimistically he endeavored to engage his students by announcing a $100,000 reward for anyone that developed a prime number generator - for the entire set.

I would like to think I was motivated by “the challenge”, however, truth be said, it was the money. I became excited. Didn’t much care for the homework, but I couldn’t wait to get home to work on it. I found my way to the dining room table, and delved into the possibilities. Numbers scattered across reams of paper, patterns everywhere – but which pattern might be “the one”?

Math is beautiful – I was enjoying the challenge, the possibilities, the patterns. When all is said and done, math and science is basically about patterns that can be interpreted and reproduced.
After a few weeks, and more paper than I had ever used for “home work”, I had distilled the patterns down to one, that worked for all prime numbers except for the lonely, even numbered - prime number of “2”. 
If I had understood back then “why” prime numbers were important, I wouldn’t have wasted another moment on “the technicality” of included “2” in the output produced by my prime number generator. Perhaps I thought like a lawyer, or a strategist, but I couldn’t take a chance that, omitting “2”, might ruin my chance of winning the reward.
I approached Mr. Taylor at school during lunch. As a prelude to my bottom line, I advised him that I had the prime number generator, then asked how I go about claiming the $100,000. 
At first he smirked as though I was pulling his leg with a sarcastic prank, then as he realized that I “wanted the money”, he arranged for me to see Dr. Harold Atkinson, the head of the math department at the University of Windsor.

Fellow classmates C. Collins and D. Girard translated this Prime Number generator into “WATFIV”, using those good ole punch cards and a large main frame computer. The printout included a large number of prime numbers as an early, pragmatically driven test of this prime number generator. These printouts along with the mathematical representation of the generator were brought to Dr. Atkinson.

Latouf's Prime Number Generator - Chapter 1 - the challenge.

Still to come:

Chapter 2 - the Validation (Tuesday, 17 May 2016)
Chapter 3 - the Generator (Thursday, 19 May 2016)

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