Tuesday, January 1, 2019

Another Perfect(ly) Large Number

Environmental & Science Education
STEM
Mathematics Education
Maths
History of Science
Edward Hessler

A perfect number is one such that its proper factors sum to the number.  The smallest is 6=1+2+3, then 28=1+2+4+7+14, followed by 496 and 8128.  These were the only ones known to the ancient Greek mathematicians but they knew there were more. They lacked the mathematics. 

These numbers are not easy to locate and further to verify. Perfect numbers are named after the French monk Marin Marsenne. While he made a mistake in a search for one his name has remained attached to these numbers. 

The Great Internet Mersenne Prime Search (GIMPS) just announced the finding of the 51st prime.  It is a big, big, big, big number. Lawrence Shirley who posted about it on his blog denoted its size this way: "The new perfect number has 49,724,096 digits (about 78.5 mi/125 km long in a font of 10 digits/inch).  

A colleague in mathematics education at Hamline, Jim Brickwedde made the scale more personal by imagining four 78.5 mile trips from Hamline University.
  • Eastbound I-94, to the first exit to Eau Claire, WI. 
  • Northbound I-35, almost to Tobies restaurant and Bakery, Hinckley
  • Westbound I-94, to the St Joseph exit and then a little
  • Southbound 1-35, to the Hwy 14 exit south of Owatanna and then some

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