It’s prime time, today! Another mathematical oddity

By Howard Buck, Columbian staff writer

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Prime number dates

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Are you feeling it?

Something... special in the air?

Turns out July 26, 2011 is another standout date in the numbers-obsessed world of Inan Aziz, University of Portland electrical engineering professor, who gets mighty fired up about these things.

Ignore our lackluster, gray July morning (sigh). Forget, for a moment, the numbing spin of digits on the national debt clock and such.

Nope, this particular Tuesday is actually one prime, prime... and prime, day.

We’ll let Aziz spell it out:

“...The single full date of July 26, 2011 is extremely rare since 7262011 = 191 x 193 x 197, i.e., the product of three consecutive prime numbers! There are only 2 such dates in this (3rd) millennium and both happen to be in this (21st) century!”

OK. Feel better now?

Of course, Prof. Aziz has much more to say. Read on, for entertainment’s sake (Aziz readily concedes there’s no larger meaning to his calendar-centric hobby). Or don’t -- but, at least, acknowledge the enthusiasm here(!!)

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“The single full date number of July 26, 2011 expressed in the month/day/year date format is 7262011 and guess what, this number equals the product of three consecutive prime numbers, i.e., 7262011 = 191 x 193 x 197!! (Interestingly enough, the reverse of this date number 1102627 also equals the product of three prime numbers (but not consecutive), that is, 1102627 = 19 x 131 x 443! Fascinating!!)

Based on my calculations, the last time this type of date happened was in 1933 on August 7 (since 871933 = 89 x 97 x 101!). (Before this, it occurred in 1833 on August 27 since 8271833 = 197 x 199 x 211!)

After July 26, 2011, the next time it will occur is on December 11, 2039 (since 12112039 = 227 x 229 x 233). Then, the next one will be in year 3121!! (January 11, 3121 expressed as 1113121 = 101 x 103 x 107!) This shows the rarity of such a date! Amazing!

So, to summarize, there are only 2 such dates in this (21st) century! Not only that, there are only 2 such dates in this (3rd) millennium (the same ones)!

Note that as an aside, there are other single full date numbers (still very seldom occurrence) which equals the product of two, four, or more consecutive prime numbers. For example, in this century, September 27, 2009 expressed as 9272009 = 3041 x 3049! This date is passed and I guess no one noticed its unique property. Similarly, February 6, 2087 written as 2062087 = 1433 x 1439! Also, March 7, 2091 expressed as 372091 = 607 x 613! Note that some of these dates can also be interpreted in the day/month/year date format. Also, in the day/month/year date format, the full date number of 19 March 2019 written as 1932019 = 1381 x 1399! As you can see, these type of dates also occur very seldom!

Also, in last (20th) century, April 7, 1953 (or 4 July 1953 in day/month/year date format) expressed as 471953 = 683 x 691! Also, 381923 = 617 x 619! Also, next (22nd) century, 412163 (which is April Fool’s Day in 2163!) = 641 x 643!

Also, interestingly enough, the product of five consecutive prime numbers yield 31 x 37 x 41 x 43 x 47 = 2022161 (i.e., February 2, 2161) which is a date common in both (month/day/year and day/month/year) date formats to occur next century! This is the closest date to occur that equals the product of the highest number of consecutive prime numbers!”

(For a chart, and more detailed analysis, download the "Prime number dates" document, above left.)