Problem of the Week 793:

Superprimes

A superprime is an integer (such as 7331) such that all its left-to-right initial segments are prime (for 7331 the segments are 7, 73, 733, and 7331, all prime). There is a largest superprime. Find it.

Source: Don Piele (U. of Wisc. at Parkside), who saw it on the USA Computing Olympiad, Qualifying Round Feb 9-16, 1995, and used it in his recent column in "Mathematica in Education & Research".

Extra Credit for the Ambitious. But beware, one of the following is an open question!

How many superprimes are there? Largest?

What about Hebrew superprimes? These work in the opposite direction, i.e., right to left. 907 is a Hebrew superprime because 7, 07, and 907 are prime. (Slight abuse of terminology because we do not actually read from right to left, just slice from right to left.)

How many Hebrew superprimes? Largest?

And now for bilingual superprimes! How many? Largest?

Speaking of Hebrew superprimes, newcomers to my list might enjoy a problem I posted a couple of years ago: How many years have there been (after 0) that are palindromic in both the Hebrew and standard calendars?

Hint: We just passed the Hebrew New Year, and we are now (mid-October 1995) in the Hebrew year 5756. There are exactly three such doubly palindromic years. Note the application: A standard palindromic year is nice for Hebrew writing in which the standard year is inserted in western numerals, for Hebrew readers then need not change their direction of eye travel. A doubly palindromic year seems even better, for one could also insert the Hebrew version into an English text and the direction of eye motion would stay the same!

Back to the Fall 1995 PotW Archive.

Jeff Erickson (jeffe@cs.berkeley.edu)
Last update: 08 Mar 96