Wow!
Monday’s centennial show broke records in more ways than one!
I managed to capture the largest audience of my show ever, so thanks to everyone for tuning in. It also captured the most international audience for the station ever with over 80% of listeners outside the UK.
I’m impressed and humbled by how far I’m reaching and I’d like to thank you all for being a part of it.
Don’t forget that there’s still plenty of time to enter our awesome competition!
NUMBERS
32,145,679,859,175,393,271
thirty two quintillion ,
one hundred forty five quadrillion ,
six hundred seventy nine trillion ,
eight hundred fifty nine billion ,
one hundred seventy five million ,
three hundred ninety three thousand ,
two hundred seventy one
95,175,236,459,876,543,216,783,825,739,834
ninety five nonillion ,
one hundred seventy five octillion ,
two hundred thirty six septillion ,
four hundred fifty nine sextillion ,
eight hundred seventy six quintillion ,
five hundred forty three quadrillion ,
two hundred sixteen trillion ,
seven hundred eighty three billion ,
eight hundred twenty five million ,
seven hundred thirty nine thousand ,
eight hundred thirty four
789,541,236,547,895,134,649,657,614,257,851,345,157,794,531,321,456,789
seven hundred eighty nine sexdecillion ,
ive hundred forty one quindecillion ,
two hundred thirty six quattuordecillion ,
five hundred forty seven tredecillion ,
eight hundred ninety five duodecillion ,
one hundred thirty four undecillion ,
six hundred forty nine decillion ,
six hundred fifty seven nonillion ,
six hundred fourteen octillion ,
two hundred fifty seven septillion ,
eight hundred fifty one sextillion ,
three hundred forty five quintillion ,
one hundred fifty seven quadrillion ,
seven hundred ninety four trillion ,
five hundred thirty one billion ,
three hundred twenty one million ,
four hundred fifty six thousand ,
seven hundred eighty nine
Answer to Integer Sequence Puzzle #4
This is the answer to the Integer Sequence Puzzle posted on Saturday.
A004231 - a(n) = n^n^n^…^n (with n n’s).
1, 4, 7625597484987, …
What is the biggest number you know of? Googol? Googolplex? In 1976, in a somewhat tongue-in-cheek article, Donald Knuth invented his up-arrow operator. Multiplication is repeated addition: 3 x 4 is the same as adding 3 to itself four times. In the same way, exponentiation is repeated multiplication: 34 is the same as multiplying 3 by itself four times. Knuth extrapolated an operation (for which he used an arrow pointing upward to represent) that would be repeated exponentiation. So 3 ↑ 4 would be 3333. The sequence above is a(n) = n ↑ n.
The value of a(3) is pretty big, but it’s nothing compared to a(4) = 4 ↑ 4 . It has 8.07 × 10153 digits. Yes, it’s got 1050 times more digits than googolplex. But single-up arrows is only the start of a rabbit hole of inconceivably large numbers. Knuth took it farther: Two up-arrows are equivalent to repeated up arrows: n ↑↑ n = n ↑ (n ↑ (… ↑ n)) with n layers of up-arrows.
The following year (1977), a Ronald Graham paper took up-arrow notation to absurd heights. In some work on a certain vertex-coloring problem in hypercubes, he showed the maximum bound was a number (he called it G, but it is commonly known as Graham’s Number) that could only be built with layers of recursive up-arrows. The first layer was 3 ↑↑↑↑ 3 (that number is already insanely large). The second layer had that many arrows between two 3s. This pattern was then repeated for 64 layers, and the top layer was G.
For a long time, Graham’s number held the record for the largest number ever used in a serious peer-reviewed proof. It has since been exceeded, but none of Graham’s successors are quite as accessible. But there are also some other methods of making big numbers.
339
2339 = 1,119,872,371,088,902,105,278,721,140,284,222,139,060,822,748,617,324,767,449,994,550,481,895,935,590,080,472,690,438,746,635,803,557,888 — one tretrigintillion, one hundred nineteen duotrigintillion, eight hundred seventy-two untrigintillion, three hundred seventy-one trigintillion, eighty-eight novemvigintillion, nine hundred two octovigintillion, one hundred five septenvigintillion, two hundred seventy-eight sexvigintillion, seven hundred twenty-one quinvigintillion, one hundred forty quattuorvigintillion, two hundred eighty-four trevigintillion, two hundred twenty-two duovigintillion, one hundred thirty-nine unvigintillion, sixty vigintillion, eight hundred twenty-two novemdecillion, seven hundred forty-eight octodecillion, six hundred seventeen septendecillion, three hundred twenty-four sexdecillion, seven hundred sixty-seven quindecillion, four hundred forty-nine quattuordecillion, nine hundred ninety-four tredecillion, five hundred fifty duodecillion, four hundred eighty-one undecillion, eight hundred ninety-five decillion, nine hundred thirty-five nonillion, five hundred ninety octillion, eighty septillion, four hundred seventy-two sextillion, six hundred ninety quintillion, four hundred thirty-eight quadrillion, seven hundred forty-six trillion, six hundred thirty-five billion, eight hundred three million, five hundred fifty-seven thousand, eight hundred eighty-eight (103 digits, 1258 characters)
