What Can You Do In 156 Sundays ?

Did you know that 267 -1 was considered a prime number for more than 250 years ? I know, right.

Obviously 147573952589676412928, which is 21 digits by the way, can be multiplied by two other numbers [hint: one is a 9 digit number and the other is a 12 digit number] and therefore cannot be a prime number. Mathematicians all over the world believed that it was, for sure, a prime number. The reason was because of the guy who came up with it.

Marin Mersenne is a french mathematician who came up with the formula for generating prime numbers. Prime numbers are one the integral blocks of our universe and they are used by mathematicians for all kinds of calculations. So when Marsenne came up with a prime number generator in late 16th century it was a big deal.

267-1 was, according to Marsenne’s formula, a prime number and every single person who worked with numbers believed it to be so. Until one fine day in New Jersey, Paul Erdos stepped in front of a huge audience at a Math Conference.

I was just listening to a recent episode of This American Life, where the host, Ira Glass, talked to Paul Hoffman who wrote about this in his book ‘The Man Who Only Loved Numbers’. Hoffman says that Paul Erdos spent his entire life solving math problems. He did not have any money, any possessions and any relationships. All he did was to travel around the world and work with other mathematicians to solve the toughest problems of his time. He was fond of the line ‘Mathematician is a machine who turns coffee into theorems’.

In 1903, when Paul Erdos wrote the 9 digit and 12 digit number on a black board and started to painstakingly multiply those two massive numbers, the entire audience at the math conference sat in unnerving silence. It was obvious that he was trying to prove the one of the Marsenne’s prime number was not, in fact, a prime number and therefore, a formula that was considered iron clad for 250 years was about to be put into doubt.

Hoffman tells Ira in his show that it was one of the rarest moments when the whole conference gave a standing ovation to Paul Erdos when he finished his multiplication. Of course, he was right. the 9 digit and 12 digit number when multiplied came out to be exactly 147573952589676412928. Marsenne’s formula was broken and Paul Erdos was the man who did it.

The past part of this entire story came after this. When asked how long it took him to find the multipliers for a number as large as 147573952589676412928, Erdos’ answer was ‘3 years of Sundays’.

Imagine that for a second. He did not work on this everyday for 156 days. He worked on it every Sunday, for three years. And it only took him 156 Sundays to break a 21 digit number.

Its incredible what we can achieve if we are willing to put up an honest and consistent effort. Looks like perseverance must be the goal. Success is only the by-product.

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