Ivars Peterson's MathTrek
The record had stood for more than a decade before it was finally broken last month.
On July 24, Markus Frind, Paul Jobling, and Paul Underwood announced that they had discovered the first sequence consisting of 23 prime numbers in arithmetic progression. This surpasses the previous record of 22 primes in arithmetic progression, set in 1993.
A prime is a positive integer evenly divisible only by itself and 1. An arithmetic progression is a sequence of numbers in which each term differs from the preceding term by the same fixed amount. For example, 1, 5, 9, 13, 17, and 21 is an arithmetic progression (or sequence) in which consecutive numbers differ by 4.
A prime arithmetic progression is one in which the numbers are all primes. For example, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 is a 10-term arithmetic progression in which consecutive primes differ by 210.
The new record holder starts with the prime 56,211,383,760,397 and adds 44,546,738,095,860 for each successive term in the sequence.
To find the record-setting sequence, Frind had to develop a new search algorithm for identifying such sets of numbers. In the course of their computer search, Frind and his colleagues also discovered 20 additional sequences consisting of 22 primes in arithmetic progression.
Mathematicians have long conjectured that there exist arbitrarily long sequences of primes in arithmetic progression. But long sequences aren't easy to find, as shown by the massive effort it took to unveil just a 23-term sequence.
Puzzle of the Week
Place the numbers from 1 to 6, with one number to each circle in the triangle, so that the sum of each straight line of three circles gives the same total. Is there more than one way to do so?
For the answer, go to http://www.sciencenewsforkids.org/articles/20030827/PuzzleZone.asp.
Gardner, M. 2001. Primes in arithmetic progression. In Gardner's Workout: Training the Mind and Entertaining the Spirit. Natick, Mass.: A K Peters.
Peterson, I. 2004. Progressive primes. MAA Online (April 26).
______. 1998. A prime surprise. MAA Online (March 23).
Information about prime arithmetic progressions can be found at http://mathworld.wolfram.com/PrimeArithmeticProgression.html and http://primes.utm.edu/glossary/page.php?sort=ArithmeticSequence.
The announcement of the discovery of 23 primes in arithmetic progression can be found at http://primes.plentyoffish.com/.
A collection of Ivars Peterson's early MathTrek articles, updated and illustrated, is now available as the Mathematical Association of America (MAA) book Mathematical Treks: From Surreal Numbers to Magic Circles. See http://www.maa.org/pubs/books/mtr.html.
Comments are welcome. Please send messages to Ivars Peterson at firstname.lastname@example.org.