I have created a new Prime number Sieve that I would like to see programmed and optimized into an executable capable of being ran on windows. I would like the finished executable emailed to my email address as an attachment file. Here is how the Prime sieve works. It makes one pass through the odd numbers unlike Eratosthenes sieve which needs to make multiple passes through numbers based on some upper bound. It also ignores all even numbers. The sieve starts at the first odd number after the number 1 which is 3 and from there after it performs operations at each succeeding odd number. The mathematical operations done at each odd number give odd number results which are non-prime. All the other odd numbers left out of the sieve are the prime numbers. So here is how it looks. It's a simple pattern that follows the odd number progression and ends the operations at each successive odd number when the perfect square occurs.
3 5 7 9 11 13 15 17 etc....
3x3=9 5x3=15 7x3=21 9x3=27 11x3=33 13x3=39 15x3=45 17x3=51
5x5=25 7x5=35 9x5=45 11x5=55 13x5=65 15x5=75 17x5=85
7x7=49 9x7=63 11x7=77 13x7=91 15x7=105 17x7=119
9x9=81 11x9=99 13x9=117 15x9=135 17x9=153
11x11=121 13x11=143 15x11=165 17x11=187
13x13=169 15x13=195 17x13=221
15x15=225 17x15=255
17x17=289
This sieve can also be optimized to remove all results AND operations surrounding numbers ending with 5 as we know without thinking that any odd number ending with a 5 is not a prime number as it is divisible by some multiple of 5. So here is the sieve again only with the 5's operations being removed.
3 5 7 9 11 13 15 17 etc....
3x3=9 no 7x3=21 9x3=27 11x3=33 13x3=39 no 17x3=51
operations skip skip skip skip operations skip
7x7=49 9x7=63 11x7=77 13x7=91 17x7=119
9x9=81 11x9=99 13x9=117 17x9=153
11x11=121 13x11=143 17x11=187
13x13=169 17x13=221
skip
17x17=289
I would like a programmer to program this sieve and optimize it with great code to operate at blazing speeds. There is no need like with Eratosthenes sieve for bounds but I'm ok with bounds being placed in the program. I would like the sieve to be able to reach prime numbers with at least 100 million digits. So some fancy coding may need to be done in order to achieve that as numbers that large and calculations that large require better memory storage.
I have gone through the description. This topic comes under Number Theory and have knowledge on the same.
I am comfortable in working on C, C++, Java, Python. Have an experience of 3.5 years as Developer.
Thank You. Looking forward to work with you.