Wednesday - fun - factoring
Dearest grandchildren and friends,
I have several hobbies. I gave one up late last spring because I finally satisfied myself that I had completed my work (or it completed me). I have been trying since highschool (say "maaaaaaany years") to factor products of two large primes when I don't know what the primes were. That sounds funny because it would seem hard to forget what primes I used but I multiply the primes on a calculator then feed the number to a program - and the program does not know what the two primes are.
Anyway, I was sure that I could solve a problem that no one else had had success with. I continued to believe in this because in highschool my math teacher told me that someone had proved that an angle could not be trisected but just a few years later I heard that someone did it!! You can find out more here and here and here. Well, whoever said that they trisected an angle was wrong! But that led me to much research on the factoring and lots of fun trying.
Back to the program! I used several processes which I had a good understand of from my maaaaaany years (there is that phrase again) of solving business problems with a computer. As each process failed to produce the desired results, I had more hope in the next. Then I ran out of processes. And hope. But I learned a great deal.
The magnitude of the problem is great - even for a powerful computer. A large prime is typically held in a register of 64 bits or greater. If a single count (say from 0 to 1) represented stepping a distance of one nano-meter (one billionth of a meter) then the number of steps required to look at every number would take us 1/10 of the way from the earth to the sun. One can see this quite simply by observing that 10 bits will hold numbers up to just over 1000 therefor 30 bits will hold numbers up to just over a billion ( 1,000,000,000) and a billion nano-meters is a meter or about a yard or about three feet. Well, we have used up 30 of the 64 bits so we still have to go over a billion times farther or 3 billion feet. Now, we have just 4 bits left which will hold a count of 16 making 48 billion feet (16 * 3). There are 5300 feet in a mile so 48 billion feet is 9 million miles or 1/10 of the way to the sun. If the computer could step the first meter in a second then 16 billion seconds would be required to complete all the steps. That is 185,185 days or 507 years. A big problem. I was looking for a shortcut but did not find one. Oh! Wait! I have another idea... Just kidding.
Love,
G'pa Bob
I have several hobbies. I gave one up late last spring because I finally satisfied myself that I had completed my work (or it completed me). I have been trying since highschool (say "maaaaaaany years") to factor products of two large primes when I don't know what the primes were. That sounds funny because it would seem hard to forget what primes I used but I multiply the primes on a calculator then feed the number to a program - and the program does not know what the two primes are.
Anyway, I was sure that I could solve a problem that no one else had had success with. I continued to believe in this because in highschool my math teacher told me that someone had proved that an angle could not be trisected but just a few years later I heard that someone did it!! You can find out more here and here and here. Well, whoever said that they trisected an angle was wrong! But that led me to much research on the factoring and lots of fun trying.
Back to the program! I used several processes which I had a good understand of from my maaaaaany years (there is that phrase again) of solving business problems with a computer. As each process failed to produce the desired results, I had more hope in the next. Then I ran out of processes. And hope. But I learned a great deal.
The magnitude of the problem is great - even for a powerful computer. A large prime is typically held in a register of 64 bits or greater. If a single count (say from 0 to 1) represented stepping a distance of one nano-meter (one billionth of a meter) then the number of steps required to look at every number would take us 1/10 of the way from the earth to the sun. One can see this quite simply by observing that 10 bits will hold numbers up to just over 1000 therefor 30 bits will hold numbers up to just over a billion ( 1,000,000,000) and a billion nano-meters is a meter or about a yard or about three feet. Well, we have used up 30 of the 64 bits so we still have to go over a billion times farther or 3 billion feet. Now, we have just 4 bits left which will hold a count of 16 making 48 billion feet (16 * 3). There are 5300 feet in a mile so 48 billion feet is 9 million miles or 1/10 of the way to the sun. If the computer could step the first meter in a second then 16 billion seconds would be required to complete all the steps. That is 185,185 days or 507 years. A big problem. I was looking for a shortcut but did not find one. Oh! Wait! I have another idea... Just kidding.
Love,
G'pa Bob
posted by G'pa Bob | 2:59 AM
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