powersoftwo's Answer Page

[two-to-the-nth]

meta

My main blog posts are getting a little long and unwieldy and I’m thinking of putting most of the text behind a “Keep reading”. Thoughts?

[two-to-the-nth]

thanks for just doing what you do. you always make me smile :)

Thanks for the feedback!

[powersoftwo]

565

2565 = 120 766 797 594 289 323 271 729 746 591 624 604 509 341 479 053 326 093 708 038 601 607 859 973 196 548 763 266 756 055 205 685 080 561 326 988 000 984 443 036 792 658 708 157 593 364 241 965 896 045 846 273 396 780 650 463 232 — one hundred twenty quinquinquagintillion, seven hundred sixty-six quattuorquinquagintillion, seven hundred ninety-seven trequinquagintillion, five hundred ninety-four duoquinquagintillion, two hundred eighty-nine unquinquagintillion, three hundred twenty-three quinquagintillion, two hundred seventy-one novemquadragintillion, seven hundred twenty-nine octoquadragintillion, seven hundred forty-six septenquadragintillion, five hundred ninety-one sexquadragintillion, six hundred twenty-four quinquadragintillion, six hundred four quattuorquadragintillion, five hundred nine trequadragintillion, three hundred forty-one duoquadragintillion, four hundred seventy-nine unquadragintillion, fifty-three quadragintillion, three hundred twenty-six novemtrigintillion, ninety-three octotrigintillion, seven hundred eight septentrigintillion, thirty-eight sextrigintillion, six hundred one quintrigintillion, six hundred seven quattuortrigintillion, eight hundred fifty-nine tretrigintillion, nine hundred seventy-three duotrigintillion, one hundred ninety-six untrigintillion, five hundred forty-eight trigintillion, seven hundred sixty-three novemvigintillion, two hundred sixty-six octovigintillion, seven hundred fifty-six septenvigintillion, fifty-five sexvigintillion, two hundred five quinvigintillion, six hundred eighty-five quattuorvigintillion, eighty trevigintillion, five hundred sixty-one duovigintillion, three hundred twenty-six unvigintillion, nine hundred eighty-eight vigintillion, novemdecillion, nine hundred eighty-four octodecillion, four hundred forty-three septendecillion, thirty-six sexdecillion, seven hundred ninety-two quindecillion, six hundred fifty-eight quattuordecillion, seven hundred eight tredecillion, one hundred fifty-seven duodecillion, five hundred ninety-three undecillion, three hundred sixty-four decillion, two hundred forty-one nonillion, nine hundred sixty-five octillion, eight hundred ninety-six septillion, forty-five sextillion, eight hundred forty-six quintillion, two hundred seventy-three quadrillion, three hundred ninety-six trillion, seven hundred eighty billion, six hundred fifty million, four hundred sixty-three thousand, two hundred thirty-two (171 digits, 2199 characters)

[antigoneprogone]

bottles of beer on the wall, one hundred twenty quinquinquagintillion, seven hundred sixty-six quattuorquinquagintillion, seven hundred ninety-seven trequinquagintillion, five hundred ninety-four duoquinquagintillion, two hundred eighty-nine unquinquagintillion, three hundred twenty-three quinquagintillion, two hundred seventy-one novemquadragintillion, seven hundred twenty-nine octoquadragintillion, seven hundred forty-six septenquadragintillion, five hundred ninety-one sexquadragintillion, six hundred twenty-four quinquadragintillion, six hundred four quattuorquadragintillion, five hundred nine trequadragintillion, three hundred forty-one duoquadragintillion, four hundred seventy-nine unquadragintillion, fifty-three quadragintillion, three hundred twenty-six novemtrigintillion, ninety-three octotrigintillion, seven hundred eight septentrigintillion, thirty-eight sextrigintillion, six hundred one quintrigintillion, six hundred seven quattuortrigintillion, eight hundred fifty-nine tretrigintillion, nine hundred seventy-three duotrigintillion, one hundred ninety-six untrigintillion, five hundred forty-eight trigintillion, seven hundred sixty-three novemvigintillion, two hundred sixty-six octovigintillion, seven hundred fifty-six septenvigintillion, fifty-five sexvigintillion, two hundred five quinvigintillion, six hundred eighty-five quattuorvigintillion, eighty trevigintillion, five hundred sixty-one duovigintillion, three hundred twenty-six unvigintillion, nine hundred eighty-eight vigintillion, novemdecillion, nine hundred eighty-four octodecillion, four hundred forty-three septendecillion, thirty-six sexdecillion, seven hundred ninety-two quindecillion, six hundred fifty-eight quattuordecillion, seven hundred eight tredecillion, one hundred fifty-seven duodecillion, five hundred ninety-three undecillion, three hundred sixty-four decillion, two hundred forty-one nonillion, nine hundred sixty-five octillion, eight hundred ninety-six septillion, forty-five sextillion, eight hundred forty-six quintillion, two hundred seventy-three quadrillion, three hundred ninety-six trillion, seven hundred eighty billion, six hundred fifty million, four hundred sixty-three thousand, two hundred thirty-two bottles of beer! Take one down, pass it around, one hundred twenty quinquinquagintillion, seven hundred sixty-six quattuorquinquagintillion, seven hundred ninety-seven trequinquagintillion, five hundred ninety-four duoquinquagintillion, two hundred eighty-nine unquinquagintillion, three hundred twenty-three quinquagintillion, two hundred seventy-one novemquadragintillion, seven hundred twenty-nine octoquadragintillion, seven hundred forty-six septenquadragintillion, five hundred ninety-one sexquadragintillion, six hundred twenty-four quinquadragintillion, six hundred four quattuorquadragintillion, five hundred nine trequadragintillion, three hundred forty-one duoquadragintillion, four hundred seventy-nine unquadragintillion, fifty-three quadragintillion, three hundred twenty-six novemtrigintillion, ninety-three octotrigintillion, seven hundred eight septentrigintillion, thirty-eight sextrigintillion, six hundred one quintrigintillion, six hundred seven quattuortrigintillion, eight hundred fifty-nine tretrigintillion, nine hundred seventy-three duotrigintillion, one hundred ninety-six untrigintillion, five hundred forty-eight trigintillion, seven hundred sixty-three novemvigintillion, two hundred sixty-six octovigintillion, seven hundred fifty-six septenvigintillion, fifty-five sexvigintillion, two hundred five quinvigintillion, six hundred eighty-five quattuorvigintillion, eighty trevigintillion, five hundred sixty-one duovigintillion, three hundred twenty-six unvigintillion, nine hundred eighty-eight vigintillion, novemdecillion, nine hundred eighty-four octodecillion, four hundred forty-three septendecillion, thirty-six sexdecillion, seven hundred ninety-two quindecillion, six hundred fifty-eight quattuordecillion, seven hundred eight tredecillion, one hundred fifty-seven duodecillion, five hundred ninety-three undecillion, three hundred sixty-four decillion, two hundred forty-one nonillion, nine hundred sixty-five octillion, eight hundred ninety-six septillion, forty-five sextillion, eight hundred forty-six quintillion, two hundred seventy-three quadrillion, three hundred ninety-six trillion, seven hundred eighty billion, six hundred fifty million, four hundred sixty-three thousand, two hundred thirty-one bottles of beer on the wall! 

[allthefactorials]

92

92! = 12 438 414 054 641 307 255 475 324 325 873 553 077 577 991 715 875 414 356 840 239 582 938 137 710 983 519 518 443 046 123 837 041 347 353 107 486 982 656 753 664 000 000 000 000 000 000 000 Name: Twelve sesquadragintillion, four hundred thirty-eight quinquaquadragintillion, four hundred fourteen quattuorquadragintillion, fifty-four tresquadragintillion, six hundred forty-one duoquadragintillion, three hundred seven unquadragintillion, two hundred fifty-five quadragintillion, four hundred seventy-five noventrigintillion, three hundred twenty-four octotrigintillion, three hundred twenty-five septentrigintillion, eight hundred seventy-three sestrigintillion, five hundred fifty-three quinquatrigintillion, seventy-seven quattuortrigintillion, five hundred seventy-seven trestrigintillion, nine hundred ninety-one duotrigintillion, seven hundred fifteen untrigintillion, eight hundred seventy-five trigintillion, four hundred fourteen novemvigintillion, three hundred fifty-six octovigintillion, eight hundred forty septemvigintillion, two hundred thirty-nine sesvigintillion, five hundred eighty-two quinquavigintillion, nine hundred thirty-eight quattuorvigintillion, one hundred thirty-seven tresvigintillion, seven hundred ten duovigintillion, nine hundred eighty-three unvigintillion, five hundred nineteen vigintillion, five hundred eighteen novendecillion, four hundred forty-three octodecillion, forty-six septendecillion, one hundred twenty-three sedecillion, eight hundred thirty-seven quinquadecillion, forty-one quattuordecillion, three hundred forty-seven tredecillion, three hundred fifty-three duodecillion, one hundred seven undecillion, four hundred eighty-six decillion, nine hundred eighty-two nonillion, six hundred fifty-six octillion, seven hundred fifty-three septillion, six hundred sixty-four sextillion Digits: 143 — The first and only value of n whose factorial, on Monday the 20th of June in the year 2016, has officially dominated the current largest power of two that @powersoftwo has posted up to said date. GET SHREK’D SON!

[two-to-the-nth]

Slow and steady wins the race.

[two-to-the-nth]

I'm curious: how often do you post on your main blog the next power of two? (I haven't followed for long enough to tell.) Do you just post whenever you feel like it? When you complete the text conversion method? Daily? Thank you for listening ^^

Two times a day, of course. And as I said, I have them all generated in text files on my hard drive. I just have to queue them.

[two-to-the-nth]

Is it run by a bot or does someone have to type the numbers out?

Half and half. I have all the posts generated into text files on my computer but I have to queue them manually.

[powersoftwo]

418

2418 = 676 921 312 041 214 565 326 761 275 425 557 544 784 286 395 355 423 968 547 480 366 360 991 530 225 982 818 124 993 751 490 268 451 683 933 401 113 623 918 903 558 144 — six hundred seventy-six quadragintillion, nine hundred twenty-one novemtrigintillion, three hundred twelve octotrigintillion, forty-one septentrigintillion, two hundred fourteen sextrigintillion, five hundred sixty-five quintrigintillion, three hundred twenty-six quattuortrigintillion, seven hundred sixty-one tretrigintillion, two hundred seventy-five duotrigintillion, four hundred twenty-five untrigintillion, five hundred fifty-seven trigintillion, five hundred forty-four novemvigintillion, seven hundred eighty-four octovigintillion, two hundred eighty-six septenvigintillion, three hundred ninety-five sexvigintillion, three hundred fifty-five quinvigintillion, four hundred twenty-three quattuorvigintillion, nine hundred sixty-eight trevigintillion, five hundred forty-seven duovigintillion, four hundred eighty unvigintillion, three hundred sixty-six vigintillion, three hundred sixty novemdecillion, nine hundred ninety-one octodecillion, five hundred thirty septendecillion, two hundred twenty-five sexdecillion, nine hundred eighty-two quindecillion, eight hundred eighteen quattuordecillion, one hundred twenty-four tredecillion, nine hundred ninety-three duodecillion, seven hundred fifty-one undecillion, four hundred ninety decillion, two hundred sixty-eight nonillion, four hundred fifty-one octillion, six hundred eighty-three septillion, nine hundred thirty-three sextillion, four hundred one quintillion, one hundred thirteen quadrillion, six hundred twenty-three trillion, nine hundred eighteen billion, nine hundred three million, five hundred fifty-eight thousand, one hundred forty-four (126 digits, 1612 characters)

[flyingcommunistbear-blog]

this is a good one

[two-to-the-nth]

Thank you. I think so too.

[powersoftwo]

408

2408 = 661 055 968 790 248 598 951 915 308 032 771 039 828 404 682 964 281 219 284 648 795 274 405 791 236 311 345 825 189 210 439 715 284 847 591 212 025 023 358 304 256 — six hundred sixty-one novemtrigintillion, fifty-five octotrigintillion, nine hundred sixty-eight septentrigintillion, seven hundred ninety sextrigintillion, two hundred forty-eight quintrigintillion, five hundred ninety-eight quattuortrigintillion, nine hundred fifty-one tretrigintillion, nine hundred fifteen duotrigintillion, three hundred eight untrigintillion, thirty-two trigintillion, seven hundred seventy-one novemvigintillion, thirty-nine octovigintillion, eight hundred twenty-eight septenvigintillion, four hundred four sexvigintillion, six hundred eighty-two quinvigintillion, nine hundred sixty-four quattuorvigintillion, two hundred eighty-one trevigintillion, two hundred nineteen duovigintillion, two hundred eighty-four unvigintillion, six hundred forty-eight vigintillion, seven hundred ninety-five novemdecillion, two hundred seventy-four octodecillion, four hundred five septendecillion, seven hundred ninety-one sexdecillion, two hundred thirty-six quindecillion, three hundred eleven quattuordecillion, three hundred forty-five tredecillion, eight hundred twenty-five duodecillion, one hundred eighty-nine undecillion, two hundred ten decillion, four hundred thirty-nine nonillion, seven hundred fifteen octillion, two hundred eighty-four septillion, eight hundred forty-seven sextillion, five hundred ninety-one quintillion, two hundred twelve quadrillion, twenty-five trillion, twenty-three billion, three hundred fifty-eight million, three hundred four thousand, two hundred fifty-six (123 digits, 1510 characters)

[allmenhavethestars]

Be honest. Who knew numbers this high up actually had names?

septentrigintillion is my favorite.

[two-to-the-nth]

Just wait, they get better.

[fyprogramming]

Logic Gates!

Not - “0 in, 1 out; 1 in, 0 out.  Whatever you put in, you don’t get out.”

Buffer - “If you take the not of not, you get what you put in - 0 in, 0 out, 1 in, 1 out.”

NAND - “Both inputs must be brought up to 1 to lower the output to 0.”

AND - “If you negate the result of Nand, you get And.  Both inputs must be brought up to 1 to raise the output up to 1.”

OR - “If you not both inputs, and then Nand them together, you get Or.  If either input is raised to 1, the output raises to 1.”

NOR - “Negate both inputs, nand them together, and negate the output.”

XOR - “Xor is complicated - The large weight ands the inputs together.  The medium weights negate the inputs, but are pulled up by the large one when both are 1.  When you nor those together, you get Xor “

XNOR - “This is comparatively simple - just negate the output of Xor, and you’re there!”

Video Source

Images and Text Stolen from Imgur!

[intercal]

Holy shit, whoever devised these apparati is the truest graybeard computer scientist

[powersoftwo]

345

2345 = 71 671 831 749 689 734 737 838 152 978 190 216 899 892 655 911 508 785 116 799 651 230 841 339 877 765 150 252 188 079 784 691 427 704 832 — seventy-one tretrigintillion, six hundred seventy-one duotrigintillion, eight hundred thirty-one untrigintillion, seven hundred forty-nine trigintillion, six hundred eighty-nine novemvigintillion, seven hundred thirty-four octovigintillion, seven hundred thirty-seven septenvigintillion, eight hundred thirty-eight sexvigintillion, one hundred fifty-two quinvigintillion, nine hundred seventy-eight quattuorvigintillion, one hundred ninety trevigintillion, two hundred sixteen duovigintillion, eight hundred ninety-nine unvigintillion, eight hundred ninety-two vigintillion, six hundred fifty-five novemdecillion, nine hundred eleven octodecillion, five hundred eight septendecillion, seven hundred eighty-five sexdecillion, one hundred sixteen quindecillion, seven hundred ninety-nine quattuordecillion, six hundred fifty-one tredecillion, two hundred thirty duodecillion, eight hundred forty-one undecillion, three hundred thirty-nine decillion, eight hundred seventy-seven nonillion, seven hundred sixty-five octillion, one hundred fifty septillion, two hundred fifty-two sextillion, one hundred eighty-eight quintillion, seventy-nine quadrillion, seven hundred eighty-four trillion, six hundred ninety-one billion, four hundred twenty-seven million, seven hundred four thousand, eight hundred thirty-two (104 digits, 1307 characters)

[abel-ax4]

On the duodecillion place, a 23 lies. I love it.

[itscolossal]

A 3D Printed Sundial Displays Time Like a Digital Clock

[animatedamerican]

NOW THAT’S JUST SHOWING OFF

[powersoftwo]

252

2252 = 7 237 005 577 332 262 213 973 186 563 042 994 240 829 374 041 602 535 252 466 099 000 494 570 602 496 — seven quattuorvigintillion, two hundred thirty-seven trevigintillion, five duovigintillion, five hundred seventy-seven unvigintillion, three hundred thirty-two vigintillion, two hundred sixty-two novemdecillion, two hundred thirteen octodecillion, nine hundred seventy-three septendecillion, one hundred eighty-six sexdecillion, five hundred sixty-three quindecillion, forty-two quattuordecillion, nine hundred ninety-four tredecillion, two hundred forty duodecillion, eight hundred twenty-nine undecillion, three hundred seventy-four decillion, forty-one nonillion, six hundred two octillion, five hundred thirty-five septillion, two hundred fifty-two sextillion, four hundred sixty-six quintillion, ninety-nine quadrillion, trillion, four hundred ninety-four billion, five hundred seventy million, six hundred two thousand, four hundred ninety-six (76 digits, 849 characters)

[nineoftoads]

I have a question - when there’s three zeroes all in the… I’m not sure what you would call it, where it’s the three digits clustered together. But for example, there’s zeroes in the one, ten, and hundred trillions places. Is it customary to say “trillion” as like, a place-holder, even when there is nothing in the trillions value, if that makes sense?

[two-to-the-nth]

Nope, you just skip it. For instance, it’s “one million”, not “one million, thousand”. Same principle, just much bigger numbers.

[two-to-the-nth]

Also I appreciate your tags.

[powersoftwo]

252

2252 = 7 237 005 577 332 262 213 973 186 563 042 994 240 829 374 041 602 535 252 466 099 000 494 570 602 496 — seven quattuorvigintillion, two hundred thirty-seven trevigintillion, five duovigintillion, five hundred seventy-seven unvigintillion, three hundred thirty-two vigintillion, two hundred sixty-two novemdecillion, two hundred thirteen octodecillion, nine hundred seventy-three septendecillion, one hundred eighty-six sexdecillion, five hundred sixty-three quindecillion, forty-two quattuordecillion, nine hundred ninety-four tredecillion, two hundred forty duodecillion, eight hundred twenty-nine undecillion, three hundred seventy-four decillion, forty-one nonillion, six hundred two octillion, five hundred thirty-five septillion, two hundred fifty-two sextillion, four hundred sixty-six quintillion, ninety-nine quadrillion, trillion, four hundred ninety-four billion, five hundred seventy million, six hundred two thousand, four hundred ninety-six (76 digits, 849 characters)

[nineoftoads]

I have a question - when there’s three zeroes all in the… I’m not sure what you would call it, where it’s the three digits clustered together. But for example, there’s zeroes in the one, ten, and hundred trillions places. Is it customary to say “trillion” as like, a place-holder, even when there is nothing in the trillions value, if that makes sense?

[two-to-the-nth]

Nope, you just skip it. For instance, it's "one million", not "one million, thousand". Same principle, just much bigger numbers.

[two-to-the-nth]

When I was younger, in middle school, I believe, I discovered graph paper. Never before had anything intrigued me like graph paper. The possibilities were endless. I loved numbers. I loved right angles. Each digit fit so neatly into a square… it was perfect. The only question was which numbers.

I started with squares, but I quickly got bored. Once I discovered the pattern, it wasn’t as fun. To find the next square, simply add 2n+1, where n2 is the number to add to. The numbers became predictable, the possibilities finite, my interest waned. Instead, I decided to put down 1, then multiply it by two, and so on, to see what I could find out.

These numbers were much more exciting to me. Because each digit changed each time, patterns could be formed. A string of nines would form and continue, and gradually cease. Same thing with 0s. 3s and 6s would alternate.

For instance, this sequence here, culminating in five 9s in a row, in 2422…

 I noticed that there was a pattern in the digits. Unperturbed by carried 1s from each column’s rightward neighbor, the digits followed the following pattern:

2 – 4 – 8 – 6 – repeat

With a carry constantly present in the rightward neighbor, the digits followed a different pattern:

1 – 3 – 7 – 5 – repeat

Each of the unused numbers, without carries, lead as follows:

0 – repeat

1 – 2…

3 – 6…

5 – 0…

7 – 4…

9 – 8…

With carries, the unused numbers went:

0 – 1…

2 – 5…

4 – 9…

6 – 3…

8 – 7…

9 – repeat

Thus, repeating nines were always preceded vertically by a four, then a two, and then horizontally alternating ones and sixes; and repeating zeros were always preceded with a five, then a seven, and then (horizontally) alternating threes and eights.

Gradually, this lead to a pattern of understanding, and one day I had the inspiration to create the math-free number doubling procedure.

For this, I’m going to use the following notation: “0” → “A” will mean “find all instances of the character(s) 0 and replace with the character(s) A”.

First, convert all the numbers to letters, with a placeholder character (in this case, “X”) to the left of each of the numbers greater than 4 (numbers that will cause a carry later). We reuse letters because both, for instance, 0 and 5, whether or not they have a carry, point to the same doubled digit.

“0” → “A”

“1” → “B”

“2” → “C”

“3” → “D”

“4” → “E”

“5” → “XA”

“6” → “XB”

“7” → “XC”

“8” → “XD”

“9” → “XE”

Next, we deal with all of the placeholder “carry” characters, replacing those numbers with their next numbers in the “carry” sequence, 1 – 3 – 7 – 5:

“AX” → “1”

“BX” → “3”

“CX” → “5”

“DX” → “7”

“EX” → “9”

Then we do the same thing with the digits that do not have a carry:

“A” → “0”

“B” → “2”

“C” → “4”

“D” → “6”

“E” → “8”

Then, finally, we deal with the leftover placeholder, which may or may not be there, at the leading digit, which means we have rolled over to the next place (and made our new number one digit longer):

“X” → “1”

Thus, the number has been doubled! No calculation required! Simple replacement of characters with other characters.

[math-is-beautiful]

I know it can be difficult to find (tumblr) math blogs, so I thought I’d try to compile a list of them. If you know of a math blog that’s not on this list, tell me about it and I’ll add it. This list will be updated as more blogs come to my attention.

Blogs that are exclusively or near...

[two-to-the-nth]

In case you're interested in other mathematical blogs. 

[powersoftwo]

2305 = 65,185,151,242,703,554,760,590,262,029,100,101,153,646,988,597,309,960,020,356,494,379,340,201,592,426,774,597,868,716,032 — sixty-five novemvigintillion, one hundred eighty-five octovigintillion, one hundred fifty-one septenvigintillion, two hundred forty-two sexvigintillion, seven…

[missbetbet-deactivated20151225]

Psshh. A google as 8 more digits than that.

[two-to-the-nth]

Just you wait until 2329...

[two-to-the-nth]

Dude, I just found this and it is awesome.You rock. It makes me somewhat curious though, about some of the things you mentioned in the Why? part. I'm wondering about the method you said used no math at all. Perhaps you could start a second blog about it and the patterns you said, it seems a shame to break this streak you have going here. For that matter, this ask would make me feel bad about breaking the streak but you don't seem to have a fanmail feature set up.

-nemosland

What is your "way to double a number without using any math whatsoever?" <3

-paintubynumbers

So you said on your Why? page you have a way of doubling numbers using no math whatsoever. Perhaps you could elaborate?

-nemosland

Well, it's a little bit of a trade secret of mine, but it involves text-based find-and-replaces. It utilizes the patterns found in powers of two to replace the digits individually with the numbered digits. I'll explain in a separate post pretty soon.