last digit of the discovered primes
i wanted to point out a little mentioned fact and tell an interesting "behind the scenes" story about SB. all the primes SB has discovered end in 7!
now, of course, the prime had to end in either a 1, 3, 7, or 9. but all five ending in 7? it's kinda strange. i may make myself look foolish here but i don't think a simple modular arithmetic trick explains it. even if all the possible primes were x (mod y) for certain k's, it doesn't seem like it would eliminate numbers with 1, 3, and 9 at a higher rate than normal.
my question to those of you interested in doing a little math right now is this: what are the odds that they would all come out 7? I know it's a statistical no-no to ask the probablity of something that already happened but humor me. if you factor the eliminated k-values, are any of them weighted with more remaining tests that end in 7? for that matter, are any of the current ones weighted either?
ok, now for the story. i've actually known that they were all 7 for awhile. I don't remember for sure if Dave and I noticed when the first two ended in 7 but I'm almost positive we noticed on the third.
i told my father about the seeming coincidence and he said something like, "you should quit wasting your time checking all the ones that don't end in 7." a couple days later he came to town and visited me at the exact moment that we discovered the fourth. he actually was the one who convinced me to check for a new prime before we went out to dinner. anyway, there it was, prime #4 and all he wanted to know was "so what does it end with?" me: "please not 7, please not 7"... and to my father's delight: 7.
the funniest one was when dave was parsing out the expansion of the 5th and my dad says "it ends in 7." dave turns to him and said something to the effect of "no. it can't be. it's over 1000:1 odds against 5 in a row." "bet you a dollar."
Dave lost a sure bet.
in the interest of saving us money in the future, someone should figure this out. ;)
was Dave just unlucky or was he doomed?
if no one has a good answer, i think i may reconsider my old man's advice and stop wasting time checking numbers that don't end in 7! :D
-Louie