Sorry if I am posting in the wrong section. I do not get where to post this query in the forum. So I am posting it here. I am working on factorization of prime product from 5 months. As I have no partner and being an average student It has been 5 months to get a formula and verifying it. I have a formula to factorize large numbers like 244,691,047,451 into two factors in a single step. I cant really promise as this work is not already there. But as internet as a limit , I have searched it I found no traces of my work. Also I wont say It is the best work for factorization at present. Because my work is not checked by anyone and I got not mathematics lecturer neat to me and who can understand me. And the work now is in an uncomplete state to give it to websites like arxiv. How large the number may be the numbers following the pattern of above number is only factorized in single step. Others need two, three and so on to factorize . What I mean is some times large numbers like above(244,691,047,451) require single step to factorize and small numbers like (581) require 3 steps to factorize. But by doing further work on it can simplify other numbers into single step. May be As being a student, having my subjects to study or may be due to weary in the persistent work, I think Now need help of some one talented like teachers or professors or researchers or students, I meant anyone. So I am free now, For masters electronics and communication student I have applied to colleges in USA, So If I am qualified in visa interview , I should go to USA in the month of August. I said it because I want help before August. As I believe there will be people from India browsing this forum. So I request anyone from INDIA, Andhra Pradesh, could help me. My name is manikanta, I am from INDIA, Andhra Pradesh, West Godavari District , Eluru. contacts: Landline : 08812-221125, mobile : 8121237097, 9440836462. U can surely catch me up on landline, But Iam not sure about mobile.
Um, 244691047451 is not the product of two primes, so finding one of its 30 non-trivial factors ( 59, 71, 167, 257, 1361, 4189, 9853, 11857, 15163, 18247, 42919, 80299, 96631, 227287, 349777, 699563, 1076573, 2532221, 3047249, 5701229, 13409933, 16137377, 20636843, 24834167, 58412759, 179787691, 952105243, 1465215853, 3446352781, 4147305889 ) is less impressive than factoring 5206192501 which is less impressive than proving to another human that 244691047499 is prime. Finally, in the field of factorization, these are not considered "large numbers" since desktop computers easily factor numbers made up of 30-digit primes, and 50 digit primes are not out of reach.
I said I have not completed my work totally. And took the above number as an example. it some times applicable for the product of two prime numbers like 3150673, 142826077 and surely it can do for very large prime numbers. But it cannot do it now, because I cannot say which numbers will have 0 loops . And it cannot prove a number is a prime number, it just factorizes. As the work is not complete I cannot surely say which numbers will be done in a single step. I am seeking help to improve my work. May be(by chance) by improving it can factorize product of two large prime numbers.
It would be more impressive if you showed how your method worked on 5206192501 or 10000000000000000000000000141007 or 4612788901088241110489338309885610592729008898152693541020459649741762187222672923167872911223544489 . It took me close to 2 days to factor the last one.
Actually if I know the numbers that can be done in zero loops, I wouldnt have asked for help. Another thing is my work is not completed, I dont know if it is at end or is at middle until it is completed. I do not have sophisticated computer or a sophisticated brain to check for large values.I can only do it for small values like 5206192501 requires 4677 or 2338 loops using %I64 format in a c program. It takes lot of time to express my ideas on the internet and I may confuse u. So I think a Person in touch is better than a person at so far. But thanks I got some new idea from ur numbers.
Not being a math student I don't understand what the importance would be of factoring such large numbers and it's application to real life situations. Care to enlighten?
If you are the only one who knows how to factor a composite number with only 2 prime factors, then you can give the composite number, N = pq, to people and they can use it to send you secret messages only you can understand. That's because the encryption function \(f(x) = x^e \, \textrm{mod} \, pq\) has decryption function \(g(x) = x^d \, \textrm{mod} \, pq\) when \(de + (p-1)(q-1)y = 1\) with all variables integers. The encryption function scrambles the numbers \( \lceil\sqrt[e]{N} \rceil..(N-\lceil\sqrt[e]{N} \rceil)\) in a way that can't be easily undone if p and q are unknown. Trivial example. e = 3, N = 55 -- then d might be 27. f(4) = 9, f(5) = 15, f(6) = 51 ... f(48) = 42 , f(49) = 4, f(50) = 40 g(9) = 4, g(15) = 5, g(51) = 6 ... g(42) = 48, g(4) = 49, g(40) = 50 So \(g(f(x)) = (x^3)^{27} \, \textrm{mod} \, 55 = x^{81} \, \textrm{mod} \, 55 = x \, \textrm{mod} \, 55\) and decryption works, because only we can compute d, because only we know \(N = 5 \times 11\). Naturally, practical applications use bigger primes than 5 and 11 -- bigger even than the 50 digit primes it took me almost 2 days to find in the ~100 digit number in this thread. References: Clay Mathematics Institute poster "The Primes Go On Forever" http://www.claymath.org/publications/posters.php http://people.csail.mit.edu/rivest/Rsapaper.pdf
It's critically important for data encryption and computer security. I'm sure it has other practical applications too.
