PRIME NUMBER OBSERVATION

[MoezHassid]

Moez Hassid 12-26-19

DEGRE: BA in Computer Since, BE in Electrical Engineering, Research in Math

Email: isdnetw@gmail.com


PRIME NUMBER OBSERVATION

Acknowledgments:
I read the book “An Introduction to Number Theory” by Professor Edward B. Burger and came up with what I believe to be a faster way to calculate prime numbers. I am not a mathematician but this book gave me the following idea which I am hoping can help solve problems related to prime numbers:


1) Number 2 is the base of all prime numbers and I would call it prime seeds.
2) If we subtract 3 from any prime number we get an even number. Since the last digit of prime numbers can be 1 like 11-3=8=2*4 or 3 like 13-3=10=2*5 or 7 like 17-3=14=2*7 or 9 like 19-3=16=2*8. From this observation we can write the following formula: 2 * X = Prime – 3 or if we add 3 to both side of the equation we get the following: Prime = 2*X+3, where X can not be any natural number. If we were to plug numbers into the above equation starting with the number 0, the following trend can be observed: Prime = 2*0+3=3, Prime=2*1+3=5, Prime=2*2+3=7, Not_Prime=2*3+3=9, Prime=2*4+3=11, Prime=2*5+3=13, Not_Prime=2*6+3=15, Prime=2*7+3=17, Prime=2*8+3=19, Not_Prime=2*9+3=21, Prime=2*10+3=23. As shown, the natural numbers 3, 6, 9 (i.e. the Lucky Tesla Numbers) do not generate prime numbers by this formula, but the number results which are 9=3*3, 15=3*5, and 21=3*7 are multiplication of two prime numbers. Below I will show how this helps to calculate prime numbers faster.
3) According to Golbach, the sum of any two prime numbers is an even number. Furthermore, if you subtract any two prime numbers the result is an even number.
4) If we multiply any two prime numbers the result is an odd number
5) The prime numbers in every set of ten digits are either all odd or all even. Example: In the set of numbers between 1-10, the numbers 3,5,7 are odd. In the next set (numbers 11-20), the sum of the digits of the prime numbers are even: 11=1+1=2, 13=1+3=4. 17=1+7=8, 19=1+9=10. In the next ten digits: 23=2+3=5, 29=2+9=11 are odd numbers. If within the ten digit set there are no prime numbers and the previous set was even, the set following will be even.
6) Every hundred digit boundary does not follow Rule 5, rather, the following pattern: the two adjacent numbers are either Even, Even or Odd, Odd. For example: 97=9+7=16 and 101=1+0+1=2 are even numbers whereas 599=5+9+9=23 and 601=6+0+1=7 are odd numbers.
7) Every 1000 digit boundary follows Rule 5. For example 997=9+9+7=25 and 1009=1+0+0+9=10 are odd, even whereas 1999=1+9+9+9=28 and 2003=2+0+0+3=5 are even, odd.


By using the formula mentioned above, I wrote a simple program that generates prime numbers faster by checking a given number and seeing if it is divisible by previously generated prime numbers.

Upon request the code to generate prime number using above formula is provided.

By using this code I was able to generate the first 100 prime numbers only using the first 9 prime numbers, the first 1000 prime number using the first 23 prime numbers, the first 10000 using the first 66 prime numbers, and the first 100000 prime number using the first 189 prime numbers.

Please review the above and Email me at

isdnetw@gmail.com.

Thank You

.

[Guest]

"1) Number 2 is the base of all prime numbers and I would call it prime seeds."
I have no idea what you mean by "base" of all prime numbers. It is the smallest prime number but that is no special observation!

"2) If we subtract 3 from any prime number we get an even number."
This not true. 2 is a prime number and 2- 3= -1 is not prime. Of course, every other prime is odd since other primes cannot have a factor of 2 and subtracting an odd number from an odd number gives an even number.

"3) According to Golbach, the sum of any two prime numbers is an even number. Furthermore, if you subtract any two prime numbers the result is an even number."
Goldbach never said such a thing and it is not true. Again you are forgetting that 2 is a prime number.

"4) If we multiply any two prime numbers the result is an odd number"
Again, not true. 2 times any other prime number is even.

"5) The prime numbers in every set of ten digits are either all odd or all even."
This is so awkwardly stated it is hard to know what you mean. You say "every set of 10 digits you apparently mean "10 numbers" not "10 digits". And in youR examples, you take the sum of digits in each prime number which was not mentioned in the statement.

"Example: In the set of numbers between 1-10, the numbers 3,5,7 are odd. In the next set (numbers 11-20), the sum of the digits of the prime numbers are even: 11=1+1=2, 13=1+3=4. 17=1+7=8, 19=1+9=10. In the next ten digits: 23=2+3=5, 29=2+9=11 are odd numbers. If within the ten digit set there are no prime numbers and the previous set was even, the set following will be even.
6) Every hundred digit boundary does not follow Rule 5, rather, the following pattern: the two adjacent numbers are either Even, Even or Odd, Odd. For example: 97=9+7=16 and 101=1+0+1=2 are even numbers whereas 599=5+9+9=23 and 601=6+0+1=7 are odd numbers.
7) Every 1000 digit boundary follows Rule 5. For example 997=9+9+7=25 and 1009=1+0+0+9=10 are odd, even whereas 1999=1+9+9+9=28 and 2003=2+0+0+3=5 are even, odd."
I simply do not understand what "6" and "7" are saying. They both refer to "Rule 5" but "Rule 5" dealt with sets of 10 numbers, not pairs of numbers.