I think we tried to direct you in the past towards arbitrary precision integer arithmetic for your calculations, as you chose to deviate Is this not an inconsistent statement? John A.

Hi All -- Regarding primes ... I believe there's no way to do anything at all with primes unless all your numbers are accurate to (at least) 2^0, that is, they are integers. (Otherwise you don't even know if they're even or odd!) So if you're using floating point numbers, you are limited to the size of your mantissa; which might be a convenient way to get something bigger than 32 bits, but it won't get you any bigger than your mantissa. (Well, you get one bit for free if your floating point representation uses the implied leading zero.) So I'm with the others: Knuth + arbitrary precision. There are some other good books on specifically arithmetic with primes. May I ask what it's for? Best regards, J.

First of all, the reason is "FOR FUN", the most practical of all reasons. Second, the basic problem is that the FORTRAN 77 routines for the PDP-11 under RT-11 are not even accurate beyond about 12 places of precision using FORTRAN 77 floating point conversions. So even if the value is correct internally to the 56 bit mantissa of the 64 bit floating point value, it is not possible to depend on the displayed result. Third, arbitrary precision routines have too much precision relative to what I actually require most of the time - which is only about 80 to 120 bits for integers. The area I am interested in is probably best described by the information at: which has a 22 digit number as the biggest value in all the tables there. So 128 bit integers which require only 16 bytes are more than sufficient. The required subroutines are easy to code in MACRO-11 and will be suitable for what I need without the added overhead of subroutines that can handle numbers with thousands of digits, let along millions. The biggest problem that I have encountered thus far was how to encode such a large integer for output. The standard method for small numbers is to just subtract powers of ten. But I needed a table of 16 bit values to place in each if the approximately 38 entries in the table, each entry being 8 * 16 bit words. So I just used the subroutine that performs addition on 128 bit values to produce the powers of ten and then use the FORTRAN 77 octal output to write the 8 word entries to a file. That file was then used in the MACRO-11 program. Actually quite a reasonable way to let the computer do the accounting details while I did the program to use the table. I realize that I omitted the actual size of the words I want to work with ( i.e. 128 bit integers) which are actually quite small compared to the really huge stuff which deals with and handles values with over a million decimal digits. For that, I apologize. Best regards, Jerome Fine

I was told that one of the first programs that EDSAC ran printed out a table of integers and their squares. This did not impess other academics at Cambridge very much, because squaring was fairly easy to do on an analogue machine (so why bother with the more complicated digital ones?) The second prgoram printed out a list of prime numbers. Other people were impressed. Doing that was very difficult on an analogue computer, so here was something the digital machine could do that the analogue one couldn't. -tony