from the outside, but then I let my mind drift free until I was hearing the conversation rather than typing and then reading it. I got inside the experience.
âWhat are the two Russian pieces we have?â Dennis asked.
âWell, thereâs the Russian remailing service,â Sky said, âand now this software company that Gerald and Pablo were apparently doing some work for.â
âOkay,â Dennis said, ânow letâs look at the numbers involved in both of those. I mean four-e-four and EES .â
âThose arenât numbers,â Lulu said.
âSheâs right,â Scarface said.
âWe may be on the wrong track altogether with this Russian business,â Dieter said. âThere is a more obvious sinister secret group.â
Dennis hurried on before Dieter could turn the discussion away from the Russians. âIn fact,â he said, âfour-e-four is a number. Itâs just in hex. That is, itâs in base 16. Look, it consists of 4 times 256 plus 14 times 16 plus 4 or 1252.â
âAnd what does that tell us?â Sky wondered.
âI donât know,â Dennis said. âLetâs play with it and see what we get. First the prime factors.â
He pulled a line out of the air and stretched it open and it became a chalkboard. We formed a semicircle around Dennis, and he put some numbers on the board.
313 times 2 times 2 equals 1252
âHere we have the parts of 1252 that can be divided no further,â he said.
Lulu raised her hand.
âYes?â
âI donât see where youâre going with this.â
âYouâre missing the point,â Dennis said. âWhat weâre doing is just poking around to see what the numbers might tell us. How do I know what weâll find until we find it? Letâs go on.â
âGrumble.â
âWho said that? Oh, never mind. Look.â Dennis wrote on his chalkboard again.
2 313 2
âIâve rearranged the factors symmetrically,â he said. âThe other possibilities are these.â
22 313
313 22
âLetâs take each one in turn. What are the prime factors of 23132?â He made a calculator appear and divided 23132 by 2 and got 11566 and divided that by 2 and got 5783. âNow is 5783 prime?â
We watched his eyes roll in his head while he figured it out. The rolling eyes in his superhero head were just for show. What he was really up to (and we all knew it but were too polite to say so) was slipping back out into Pabloâs system, locating a programming language (C++ was all Pablo had on hand) and writing a quick routine that would take the square root of any number and then divide that original number by successive odd numbers until it either found a number that divided the original number evenly, in which case the original number wasnât prime, or a number that was bigger than the square root, in which case the original number was prime.
Dennis used the program on 5783 and found that it was prime and brought his rolling eyes to a halt.
âSo 2 times 2 times 5783 is 23132,â he said.
âAnd that tells us exactly what?â Dieter said.
âWell, nothing, that I can see,â Dennis said. âNegative results can be productive, too, you know. Letâs go on.â
âSigh.â
âWho said that?â Dennis glared around at us for a moment. Then he turned back to the board, and using the prime routine on 22313, produced the factors 53 and 421 both of which turned out to be prime. Then he divided 31322 by 2 and got 15661 which turned out to be prime.
âThis had all better add up to something,â Scarface said. He made something that looked like blood run off his bat fangs.
âHey, thatâs a good idea!â Dennis said. âLetâs add up one instance of each of the prime factors from all the numbers.â
âWow, look at that. Three twos and two threes!â Dennis said. âNow if