HOW MANY CALCULATIONS AT ONCE??

[snail]

Each computer works on a unique exponent which nobody else is testing at the same time.

Your computer is working on the exponent M19463987 which is a 5.8 million digit number. You are the only one working on that number right now. At the end of your test (approximately 4 weeks), you will know whether or not that number is prime. If it is prime, bells will go off, someone else will double check your exponent to be sure there were no errors during your test, and if it is verified that the number is in fact prime, you will be given credit for its discovery. If your LL test shows that number isn't prime, you are assigned a new exponent to begin testing.

Does that help?[/b]

[cheesehead]

Originally Posted by alienz

If I am working on M19463987, and each of us are working on single exponents of a 5.5 million digit number, how can any individual be responsible for finding a prime

Another explanation, from a slightly different viewpoint than snail's (as you can imagine, a snail and a llama have different viewpoints -- we're both right, but from different perspectives :) ):

The number you are working on, M19463987, equals 2^19463987-1, which means "(2 raised to the power 19463987) minus 1". That means multiply 19,463,987 2s together (2 x 2 x 2 x 2 x ... 2 x 2, where there are 19,463,987 2s), then subtract 1. When we multiply a number by itself one or more times like that, the process is called exponentiation, and the total count of the number of 2s is called the exponent.

So the exponent of M19463987 = 2^19463987-1 is 19463987, and there's only one exponent for the 5-plus-million-digit number you are working on.

You're assigned the whole 5-plus-million-digit number, not just part of it.

[ADBjester]

To add a bit more to that excellent description you just read, here's a layman's description of the work your computer is doing.

Imagine the number 17. Imagine 17 SQUARED, or 17 x 17. That's 289.

Imagine the number 72,892. Now imagine 72,892 SQUARED, or 72,892 x 72,892. That's 5,313,243,664. As you can see, when you square a number, the results get much, MUCH bigger, very quickly.

OK, now picture numbers like your exponent. Picture a number of up to 5,500,000 DIGITS, squared. That's a truly mind-boggling number.

To test your number for primality, your computer has to perform the equivalent of that operation, and then divide it by a huge number, and then work with the remainder. Those are tremendously huge mathematical operations. A typical P4 can only do the work five times every second.

Now, to test the number for primality, it has to to that work the equivalent of one time for every digit in your number -- in your case, 5.5 million times. Only the result of the last one matters. If the remainder of the very last time is zero, your number is prime.

You can't just skip to the last one, though, because each new "iteration" of the test depends on the value of the last one. The second "part" of the test has to wait for the first to complete. The third part has to wait for the second part. And so forth.

Thus, to do that huge math 5,500,000 times will take about 0.2 seconds times 5,500,000 calculations, each done in succession. That's 1,100,000 seconds, or about 305 hours, or about 12 days and 18 hours.

Your true time may vary depending on your CPU and how heavily it is working. But that's what your CPU is doing.

Now, admittedly, George (with the help of a gentleman named Fourier) has written the code to do those huge multiplications MUCH faster than doing them for real. There are special table lookups called Fourier Transforms that make the tests we're doing MUCH MUCH faster than doing the math for real -- but the results are as accurate.

If we had to take a 5.5 million digit number times a 5.5 million digit number, and then divide it by another huge number, and we had to do the math "longhand" (for real) then our tests would be much, MUCH longer than they already are. Only through the magic of these special Fourier Transformations are our tests as "short" as they are.

The last "nicety" about these tests is that as the numbers get bigger, things get tougher still. Just as 72,892 x 72,892 is tougher to calculate than 17 x 17..... an 11 million digit number times a 11 million digit number is MORE than twice as hard to figure than the numbers you're working with now.... and not only do the calculations themselves get tougher, so too do the numbers of them.

If your test was 11 million digits long, the resulting calcualtions would be about 2.3 times as difficult and lengthy... *and* there would be twice as many of them as well. So a number twice as large isn't twice as difficult to test -- it is about 4.5 times more difficult to test!

I hope this helps you understand the immensity of what you've asked your computer to do.

Have fun!

Jeff

[smh]

Now, to test the number for primality, it has to to that work the equivalent of one time for every digit in your number -- in your case, 5.5 million times.

It's even worse, for M19463987 you need to repeat this calculation 19463987-2 times

[bibiteinfo]

Originally Posted by Kevin

some of this stuff should go into an FAQ somewhere......

The number you are testing is actually 2^19463897 -1. (edit: go to http://www.mersenne.org/prime5.txt to see what 2^13466917 -1 looks like. )

To prove it's prime, you have to do recursive series. If, in this case, the 19463897th term is 0, than 2^19463897 -1 is prime. But you have to complete the whole test to figure out whether or not it ends in 0.

How can I know how many digits is my number? I have M33533807 and I would like to know how much digits it's long (And if I could see it it could be better :) like this one http://www.mersenne.org/prime5.txt)

[dswanson]

D = ceil(p*log10(2))

where...
D is the number of digits (base 10)
p is your exponent
log10 is base-10 logarithm; hence log10(2) = 0.301029996....
ceil() rounds its argument up to the next highest integer

For example, suppose p = 17
D = ceil(17*log10(2)) = ceil(5.1175...) = 6

so 2^17-1 has 6 digits. And if you pull out your calculator, 2^17-1 = 131071 (6 digits)

Similarly, suppose p = 13466917
D = ceil(13466917*log10(2)) = ceil(4053945.97) = 4053946 digits

And for your number, p = 33533807
D = ceil(33533807*log10(2)) = ceil(10094681.78 ) = 10094682 digits

[bibiteinfo]

Thanx :)
And now does a program could let me excute this function and give me the number

(I could do it in VB but I'M pretty sure that it will say me that the number is to big)

[cheesehead]

Originally Posted by bibiteinfo

How can I know how many digits is my number? I have M33533807 and I would like to know how much digits it's long

does a program could let me excute this function and give me the number

Go to the CPU Benchmarks page at http://www.mersenne.org/bench.htm. After the first three paragraphs are two rows of boxes. The first row, labelled "CPU Type", "CPU Speed", "Hours/day" and "Exponent", are the input boxes. The second row, labelled "Estimated Time" and "Decimal digits", are the answer boxes.

The answer in the "Estimated Time" box depends on what's in all four input boxes. The answer in the "Decimal digits" box depends only upon what's in the "Exponent" box.

So you can just ignore the "CPU Type", "CPU Speed", and "Hours/day" boxes, put your exponent in the "Exponent" box and press Enter. Your answer will appear in the "Decimal digits" box.

[Mr. P-1]

[quote="bibiteinfoHow can I know how many digits is my number?[/quote]

If you're only looking for an estimate, then a useful rule of thumb is to devide by 10 and multiply by 3.

Alternatively, if it was assigned by the Primenet Server, then it's a little over 10M digits. :)