I wonder how long it would take the program to finish this, factoring the entire possible range, doing just 3.

I found this site, and prime numbers ending with 3 are as common as 1 or 9. That means it's as likely to be 3 as any other number.

http://korn19.ch/coding/primes/ending.php

Don't forget, we don't really need to check all the possible numbers from 2 to the public key. The only truly likely ones will be in a certain bit range, and that is a much smaller amount than totally brute-forcing the entire number.

2.1? TI started the war by not adding an asm( command in future OS releases, or integrating ndless. 2.1 is just going a little farther.

You misunderstood my post.  I'm talking about the ending number for p and q multiplied together.  Let me brake it down further.  We know N is a semiprime, which means a multiple of two primes.  N cannot end with 2,4,5,6,8,0.  Otherwise, factorization would be trivial.  N must end in 1,3,7,9.  The way that multiplication works, the least significant digit (The right most) of the two primes multiplied together has the same last digit as N.  Like in 221.  13x17=221.  The last digit could be 1x1, 3x7, or 9x9.  We don't know if we don't have the factorization.  But we do know that the two primes must end in either both a 1, a 3 and a 7, or both end in 9.  Otherwise, it would be impossible to multiply them together to get 221, because the last digit would be different.  The only two prime numbers that can multiply to end in a 3 are 1 and 3.  That means, if the number ends in 3, like N=143, then the factors must end in 1 and 3, which they do, because 143=11x13.  It just makes it so you don't necessarily need 4 computers.

Besides, you could make it even faster than that.  If you have 10 computers, you could start them at offsets of 10, and count by 100.  If you had 6 computers, you could offset by 10 and have them count by 60.  Basically, in a distributed computing project, the server would tell each computer a number to stop at, so that each computer would again be an offset of 10 from each other, then increase the count by 10, and send it to each computer.  This way, all the computers would not have to wait for the others to finish if it was like 10,000 ahead of the rest of them.  Let me explain further.  Let's say I have computers A, B, and C.

A is at 10, B is at 20, and C is at 30.  They are each counting by 30.  Then, computer D decides to join in.  So, the server gets a request, and asks all the clients where they are at.  The server then chooses the highest one, plus some huge number to stop at.  Let's say C is the fastest, and is at 90.  D now is set to 100.  A and B go with the previous increment until A gets to 70 and B gets to 80.  Then, they use the new increment given by the server to continue.

This has been one long post.  Does this make sense?

Yeah, graphmastur, I see what you mean now. Subtracting by 10 with several computers actually isn't a bad idea, although according to this pdf, incrementing by 6 would be more efficient. More primes, less non-primes.

http://www.dozenalsociety.org.uk/pdfs/primeforms.pdf

With enough optimizations and enough pcs, perhaps this would be possible. you never know!

Server-wise, not much has to be done.....send numbers to computers, receive negatives for a set length, and send again. If a positive response is found, it immediately sends the factors to every computer doing the program, spreading the key before ti has a chance to squelch it.

Do you think TI could change the keys with an OS update? Scary thought.

At the moment, I believe boot1 gets verified by boot0, boot2 by boot1, and the OS by boot2. Each of the bootloaders has the verification code for the one above it, but that same code is signed by the one below it. So, yes, TI can change the key if they want. Also, I'm pretty sure boot0 is non-modifiable.

There's a boot0? Or is boot0 the diag menu?

With enough optimizations and enough pcs, perhaps this would be possible. you never know!

Not by TF, no, by an extremely large margin. We'd need ~1e55 times the estimated number of electrons in the universe.

Quote from: DJ Omnimaga on July 21, 2010, 07:08:29 pm

There's a boot0? Or is boot0 the diag menu?

no boot0 to my knowledge

Ok thanks.