When Frank Nelson Cole Factored A Large Number During A “Lecture”


For around 200 years, several mathematicians had surmised that the Mersenne number 267 – 1 may be prime. However, French mathematician Édouard Lucas proved in 1876 that 267 – 1 can be factored and hence, not a prime. However, he was unable to find its factors.

On October 31, 1903, Frank Nelson Cole, an American mathematician informed his fellow mathematicians that he would attempt to factorize 267 – 1 during a meeting of the American Mathematics Society. He went towards the chalkboard and proceeded to give an approximately one-hour “lecture”. Without uttering a single word, he began to calculate the value of 267 – 1 and he got 147,573,952,589,676,412,927. Moving to the other side of the chalkboard, he wrote 193,707,721 × 761,838,257,287 and he calculated the answer manually using long multiplication.

After Cole was finished multiplying the two large numbers, he was able to show that the answer equaled 267 – 1. Then he got back to his seat, not having said anything during the entire “lecture”. Despite the silence, his presentation was well-received by the audience who gave it a standing ovation.

Years later, when Cole’s friend, Eric Temple Bell, asked him how long did it take for him to factor the number, his reply was “three years of Sundays”.


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My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

12 thoughts on “When Frank Nelson Cole Factored A Large Number During A “Lecture”

  1. It takes more than half a year to get that perfect silence from the audience. He definitely deserves the ovation.

    PS: Did anyone notice why no one bother to raise a comment before and after the lecture was they had no idea what the answer is/was.


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