## Frank Morgan's Math Chat |

MATH CHAT TV, the live, call-in show with questions and prizes, will air on the web Wednesdays, January 12, 19, and 26, 7-7:30 pm Eastern time, at raserver.williams.edu/live/MathChat.rm

**VITAL SINES.** Math Chat has learned that the "unique entertainment" promised
for the opening banquet January 18 at the Washington mathematics meetings
will include the debut of the latest skit by Colin Adams. Entitled "Vital
Sines," it stars Adams, Math Chat's own Frank Morgan, and other Williams
College colleagues.

**MATH LUNACY. I found some questionable mathematics in the December 21 issue
of The Christian Science Monitor (the paper where the Math Chat column
began). An article on the moon says: "[In its closest approach to Earth,]
the moon should appear about 14 percent larger than it does when it's
farthest away from Earth. That's not even the difference between a medium
and a large pizza, and who can tell that from 221,463 miles away?" Of
course, distance has nothing to do with percentage difference in size or
brightness.**

**
Another article describes an 89-year-old man as "nearing his ninth decade."
Actually, at age 90, he will enter his tenth decade.**

**
Readers are hereby invited to send in more examples of questionable
mathematics from the media.**

**
WHAT did the number zero say to the number eight? "Nice belt." (Submitted
from Denmark for England's Millennium Vault, according to USA Today,
December 30.)**

**
OLD CHALLENGE. Justin Smith calls 5939 a "right" prime because it remains
prime after dropping any number of digits from the right: 5939, 593, 59,
and 5 are all prime. How many right primes are there less than 1000? Is
there a largest right prime?**

**
ANSWER. Joseph DeVincentis, Jim Wiechmann, Chuck Diminnie, Eric Brahinsky,
and Luke Gustafson find by exhaustive search that there are 27 right primes
under 1000 and 83 right primes in all, the largest of which is 73,939,133.
We know of no elegant proof that there are finitely many. You might suspect
that there are only finitely many, since large numbers are very unlikely to
be prime, what with all the smaller numbers which might divide them.**

**
Of course all digits of a right prime must be odd (except possibly for an
initial 2). José Cañizo Rincón notes that most digits (all but at most two)
must be 3 or 9. Indeed, for any initial segment with one 2 and one 1 or 7,
the sum of the digits and hence the number would be divisible by 3.
Similarly, an initial sequence with no 2 and three digits from {1, 7} would
be divisible by 3.**

**
Kok Seng locates right and left primes at Chris Caldwell's famous Prime
Page, called "right-truncatable" and "left-truncatable" primes. The left
primes are also finite in number (4260); the largest is**

**
**

**
Jean-Francois Peltier also notes that twelve numbers are both right and
left primes: 2, 3, 5, 7, 37, 53, 73, 313, 317, 373, 3137, 3797.**

**
NEW CHALLENGE (Chris Lang). I imagine myself sitting on a
beach in Oregon, watching the Sun set over the Pacific. At a certain
moment, the very last bit of the Sun disappears below the horizon. The
question is: Can I make that last bit of Sun reappear by jumping up quickly
to my full height, or perhaps by very quickly running up the hill behind me,
to increase the elevation of my point of view?**

**
Send answers, comments, and new questions by email to
Frank.Morgan@williams.edu, to be eligible for Flatland and other book
awards. Winning answers will appear in the next Math Chat. Math Chat
appears on the first and third Thursdays of each month. Prof. Morgan's
homepage is at www.williams.edu/Mathematics/fmorgan.**

**
Copyright 2000, Frank Morgan.
**