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On the topic of palindromic numbers, I remember being fascinated as a kid with the fact that if you square the number formed by repeating the digit 1 between 1
by gregschlom 2y ago
On the topic of palindromic numbers, I remember being fascinated as a kid with the fact that if you square the number formed by repeating the digit 1 between 1 and 9 times (e.g. 111,111^2) you get a palindrome of the form 123...n...321 with n being the number of 1s you squared.
The article talks about a very similar number: 2^31-1, which is 12345678910987654321, whereas 1111111111^2 is 12345678900987654321
- ColinWright 2y agoYou have misunderstood or mis-read the article ... 2^{31}-1 is not 12345678910987654321. Specifically, 2^{31}-1 = 2147483647. Borel asked Dyson to name a prime number and, unlike Grothendieck, Dyson provided a number that is only divisible by 1 and itself: 2^{31) – 1. But that reply did not satisfy Borel. He wanted Dyson to recite all of the digits of a large prime number. Dyson fell silent, so after a moment, Sloane jumped in and said, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1.” So Sloane was supplying a different prime, but one where he could recite all the digits.
- gregschlom 2y agoOh, thank you. Knowing very well that 2^32 is around 4 billion, I should have immediately noticed that 12345678910987654321 is way to big to be 2^31