Problems & Puzzles: Puzzles Puzzle 27.- Heinz Rectangles. Let’s define a "Heinz Rectangle" with the following example: given by Heinz in his pages http://www.geocities.com/CapeCanaveral/Launchpad/4057/primes.htm Heinz rectangle (4x5) 5 +7+11+13+17= 53 7+ 11+13+17+19= 67 11+13+17+19+23= 83 13+17+19+23+29=101 Following the pattern, this is the bigger I have found: (8x11) 3526741+ 3526771+ 3526781+ 3526793+ 3526867+ 3526909+ 3526931+ 3526933+ 3526937+ 3526949+ 3526987= 38795599 3526771+ 3526781+ 3526793+ 3526867+ 3526909+ 3526931+ 3526933+ 3526937+ 3526949+ 3526987+ 3526993= 38795851 3526781+ 3526793+ 3526867+ 3526909+ 3526931+ 3526933+ 3526937+ 3526949+ 3526987+ 3526993+ 3526997= 38796077 3526793+ 3526867+ 3526909+ 3526931+ 3526933+ 3526937+ 3526949+ 3526987+ 3526993+ 3526997+ 3527023= 38796319 3526867+ 3526909+ 3526931+ 3526933+ 3526937+ 3526949+ 3526987+ 3526993+ 3526997+ 3527023+ 3527033= 38796559 3526909+ 3526931+ 3526933+ 3526937+ 3526949+ 3526987+ 3526993+ 3526997+ 3527023+ 3527033+ 3527057= 38796749 3526931+ 3526933+ 3526937+ 3526949+ 3526987+ 3526993+ 3526997+ 3527023+ 3527033+ 3527057+ 3527059= 38796899 3526933+ 3526937+ 3526949+ 3526987+ 3526993+ 3526997+ 3527023+ 3527033+ 3527057+ 3527059+ 3527071= 38797039 Find a bigger one than this.
Jud Mc Cranie discover the following 9x21 Harvey Heinz rectangle at November 7, 1998. Here is his communication: "Add 3037590000 to the numbers on the left side of the equation. 2687+2689+2741+2743+2837+2881+2917+2951+2969+2977+3007+3011+ Two days later he mail me this: "I found some more Heinz rectangles.... I also have 9x41, 9x57, and 9x97. Do you want me to send them (they're pretty large)?" I answer him that if somebody want those huge rectangles he could send them directly, but that if he get later other rectangles of more than 9 rows I'll be glad in showing one of them them in this pages. *** But I have changed my mind and I have asked to publish his largest Heinz Square the following way: The first prime, the last prime and the sum, of each and all row. This is the 9x97 Heinz Rectangle gotten by Jud McCranie: 82114909 + ... + 82116701 = 7965228343 (each one of the 9 rows has 97 consecutive primes whose sum is a prime; the initial prime of each row is the second prime of the previous row) Can you get a Heinz Rectangle with 10 rows? (by experience: "the row" is the harder variable...) *** On December 2005, J. K. Andersen wrote:
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