Lehmer sieves - for calculating solutions to Diophantine equations

Lehmer sieves are mechanical devices that implement sieves in number theory. Lehmer sieves are named for Derrick Norman Lehmer and his son Derrick Henry Lehmer. The father was a professor of mathematics at the University of California, Berkeley at the time, and his son who followed in his footsteps, as a number theorist and professor at Berkeley.

A sieve in general is intended to find the numbers which are remainders when a set of numbers are divided by a second set. Generally, they are used in finding solutions of diophantine equations or to factor numbers. A Lehmer sieve will signal that such solutions are found in a variety of ways depending on the particular construction.

The first Lehmer sieve in 1926 was made using bicycle chains of varying length, with rods at appropriate points in the chains. As the chains turned, the rods would close electrical switches, and when all the switches were closed simultaneously, creating a complete electrical circuit, a solution had been found. Lehmer sieves were very fast, in one particular case factoring

in 3 seconds.

In the 1930s or thereabouts he was reluctantly going to a fellow professor's house for a cocktail party, to celebrate the return from China of the man's wife.  She greeted him at the door and said "You mathematicians count things, right?  Tell me something about this!" and handed him one of those insanely complicated wooden Chinese puzzles you take apart but probably will never get back together again.

He said, twirling the thing around in his hands, "Well, if you count the number of corners, and subtract all the edges, and then add the faces, you get...let's see now...you get 2!"

"Nobody can count that fast!" she said.  "I assure you it is true, madam" he replied.  She went off in a corner with some tape and a pencil.  Fifteen minutes later she said, in an astonished voice, "It's true!"

He never let on, of course.

Six Trivia Questions: Suprising Answers

Trivia Questions....Surprising Answers:
Read these 6 questions and give your answer. (.......and oh how they hate being associated with the word "socialist")
Six trivia questions to see how much history you really know.  Be honest, it's kinda fun and revealing. If you don't know the answer make your best guess. Answer all the questions (no cheating) before looking at the answers.   Happy New Year!

Who said it?

1) "We're going to take things away from you on behalf of the common good."

A. Karl Marx B. Adolph Hitler C. Joseph Stalin D. Barack Obama E. None of the above

2) "It's time for a new beginning, for an end to government of the few, by the few, and for the few...... And to replace it with shared responsibility, for shared prosperity."

A. Lenin B. Mussolini C. Nelson Mandella D. Barack Obama E. None of the above

3) "(We).....can't just let business as usual go on, and that means something has to be taken away from some people."

A.  Nikita  Khrushev B. Josef Goebbels C. Boris Yeltsin D. Barack Obama E. None of the above

4) "We have to build a political consensus and that requires people to give up a little bit of their own ... in order to create this common ground."

A. Mao Tse Dung B. Hugo Chavez C. Kim Jong Il D. Barack Obama E. None of the above

5) "I certainly think the free-market has failed."

A.  Karl Marx B. Lenin C. Molotov D. Barack Obama E. None of the above

6) "I think it's time to send a clear message to what has become the most profitable sector in
(the) entire economy that they are being watched."

A. Pinochet B. Milosevic C. Saddam Hussein D. Barack Obama E. None of the above

Scroll down for answers


(1) E. None of the above.  The statement was made by Hillary Clinton.


(2) E. None of the above.  The statement was made by Hillary Clinton


(3) E. None of the above.  The statement was made by Hillary Clinton


(4) E. None of the above.  The statement was made by Hillary Clinton


(5) E. None of the above.  The statement was made by Hillary Clinton


(6) E. None of the above.  The statement was made by Hillary Clinton


Want to know something scary? She and "I never had a sexual relationship with that woman" Bill may be the next president if you don't forward this to everyone that you know.

What a sale!

World's Oldest Running Car Sells for $4.62 M in a 3 minute bidding war.
This is the oldest motor vehicle car in the world that still runs. It was built one year before Karl Benz and Gottlieb Daimler invented the internal combustion engine.
The world's oldest running motor vehicle has been sold at auction for an astonishing $4.62 million, more than double the pre-sale estimate, as two bidders chased the price up in a three-minute bidding war.
The 1884 De Dion Bouton et Trepardoux Dos-a-Dos Steam Runabout drew a standing ovation as it was 'driven up onto the stage' at Friday's RM Auction in Hershey, Pennsylvania - to prove that this 127-year-old car really does run! - and attracted a starting bid of $500 000, which was immediately doubled to $1 million. Encouraged by the applauding crowd, the bidding went swiftly up to $4.2 million - 4.62 million including the 10 percent commission - before the car was knocked down to an 'unnamed buyer'.
The Dos-a-Dos (Back-to-Back) Steam Runabout was built in 1884 by George Bouton and Charles-Armand Trepardoux for French entrepreneur Count de Dion, who named it 'La Marquise' after his mother.
In 1887, with De Dion at the tiller, it won the world's first ever motor race (it was the only entrant to make the start line!) covering the 32 km from the Pont de Neuilly in Paris to Versailles and back in one hour and 14 minutes (an average of 25.9 km/h) and, according to contemporary reports, hitting a breathtaking 60 km/h on the straights.
La Marquise has only had four owners, remaining in one family for 81 years, and has been restored twice, once by the Doriol family and again by British collector Tom Moore in the early 1990's.  Since then, it has taken part in four London-to-Brighton runs and collected a double gold at the 1997 Pebble Beach 'd'Elegance in California'.
Count de Dion winning the first ever motor race.