It’s been known since 1876 that 2⁶⁷-1 isn’t prime, but for decades no one knew what the factors were.

Then, at a meeting in 1903, mathematician Frank Nelson Cole gave an hourlong “lecture” in which he didn’t say a word. On one chalkboard he expanded the value of 2⁶⁷-1:

147,573,952,589,676,412,927

On another he wrote:

193,707,721 × 761,838,257,287

Then he multiplied those values by hand. The two boards matched. He had found the factors. Cole returned to his seat amid a standing ovation.

He later admitted that finding the factors had taken “three years of Sundays.”