## Feller 17

At http://cosmicvariance.com/2007/01/30/the-power-of-17/ John said"... if you ask people to choose a random number between 1 and 20,inclusive ... there is a big excess at 17...".

I commented that "... William Feller (his wikipedia entry has alink to a St. Andrews biography) was born in Zagreb in 1906, got hisPh.D at Gottingen (studying under Hilbert and Courant) in 1926, andmoved to Princeton in 1950, where he told his students two thingsthat stand out in my memory:

• 1 - You always need to have in mind a concrete example to understand abstract concepts, and his favorite was the harmonic functions on the unit disk. It, and its generalizations, do exemplify MANY abstract math structures.
• 2 - It is good to have a random number to plug into equations to check out how they work numerically. The best such number is 17. 17 is prime, bigger than 12, not unlucky like 13 [ I should have added that for people who like 13, it is too lucky ] , and not too big like 19. Since the math genealogy site shows that he had 17 (of course) students and 614 descendants, maybe "The Power of 17" is due to him. At least, his spirit is doubtless happy to see that nowadays people are likely to pick his favorite number, 17. ...".

At http://scienceblogs.com/cognitivedaily/ Dave Munger said "... Iposted a poll asking readers to simply pick a number between 1 and 20... Take a look at the chart:

...[ Jim commented ]... "... True story: A friend teachinga math class years ago had derived some equation and told the classto pick a value for "x" and calculate the result. "What value"someone asked. ... "Seventeen," my friend answered. "Why seventeen?"came the inevitable query. His reply...

"Well,

• zero times anything gives you zero, so too many things will cancel out.
• One times anything doesn't change, so that's bad, too.
• Two and
• three are too small.
• Four is a perfect square so that may cause some problem.
• Five is half of ten, and anything in a decimal world is probably special.
• Six is a perfect number, so that may affect your results.
• Seven is too lucky.
• Eight is a perfect cube.
• Nine is a perfect square.
• Ten we already covered, and
• eleven is too close to ten.
• Twelve is divisible by practically everything so something is bound to cancel out.
• Thirteen is unlucky,
• fourteen is twice seven so it's too lucky.
• Fifteen we covered,
• sixteen is a perfect square and even it's square root is a perfect square.
• Eighteen is twice a perfect square.
• Anything bigger and by the time you've raised it to some power the results are too big to handle.
• That leaves seventeen!" ..."

...[ JL Wallace commented ]... "... 17 is a Full ReptendPrime, as is 7 which is weird that those two got more hits than anyother in the ... chart. ...". ...".