In Accomplishments, we have bragged about 400 sequential fully-factored numbers. We have decided to provide them here for educational value. In the downloadable .zip file are two .pdf’s and two .jpg’s. The instructions below attempt to provide anyone interested with helpful tips to evaluate them. The NFT still retains the interest of an explanation of how to factor similar large numbers on your own computer.
Looking at large numbers and their factors is kind of like looking up at a statue, without a plaque to introduce you to the name, the artist and a synopsis of what the art is meant to represent.
Some of us find it entertaining or gratifying to check the factorizations, and see if the numbers work out when you multiply them back together. After all, factoring them is the hard part: checking them is supposed to be easy.
As a practical matter, data entry for this many digits can be difficult to get right at first. They are broken up into five digit groupings, for easy reading, but in a python interpreter the numbers are all in one group, and can tend to run together. For this reason, you may find it helpful to set a separate variable equal to each factor. The images illustrate what this might look like. In python if you set 5 factors equal to a1, a2, a3, a4, and a5 respectively, then you can set a = a1 * a2 * a3 * a4 * a5, and print a. This is helpful when you enter a factor incorrectly, and the result does not come out as you want it to. It is easier to retype one factor than to retype an entire line of over a hundred numbers.
One way or another, you will need to get the large number into a variable. If you choose “x,” you can use a1 * a2 * a3 * a4 * a5, or simply set x=, and hope you typed the whole number in correctly.
On that rare occasion when a factor is wrong, you can zone in on it by modular dividing x by each factor. The result should be zero if it is a valid factor. The notation is x % a1.
Also important is that a single digit being entered incorrectly may result in the leading AND FINAL digits reading out correctly, but digits in the middle being wrong. I have shown this by example in img_341.jpg. If you leave a digit out, the result will be shorter, and the numbers will be wrong.
In closing, be sure and multiply ALL factors together. If you leave one out, the result will be too short.
When you evaluate a new number, you will need to add 1 to x, with a statement like x = x + 1.
When you are evaluating the pdf’s, you can re-use a1, a2, a3 etc as much as you want. I used five separate variables for clarity.
Due to clerical errors, some of the original entries were defective. The second pdf contains an exhaustive list of corrections. I hope you have a lot of fun multiplying the numbers together, and finding my mistakes.