## 73 – the best number?

I was convinced that 42 is a  funny number but the last episode  of  “The Big Bang Theory” (4×10: The Alien Parasite Hypothesis) taught me that 73 is  much more fascinating.  Far from being addicted to numerology or the strange ideas of Paul Kammerer I just like number games and number theory.

Sheldon Cooper considers 73 being the best number because switching digits, 73 (21st prime number) becomes 37 (12th prime number). The number 21 includes factors 7 and 3. Seventy-three in binary (1001001) is a palindrome.

The episode aired on December 9th 2010.  On December 10th the aforementioned facts were added to the Wikipedia article about 73.

Meanwhile other properties were added (as of December 12th 2010): Of the 7 binary digits representing 73, there are 3 ones. Also, 37+12=49 (seven squared) and 73+21=94=47*2, 47+2 also being equal to seven squared.

Looking behind the scences, one finds further coincidences: Sheldon’s discussion of 73 appears in the overall 73th episode of the series and Jim Parsons – the actor portraying Sheldon – was born in 1973 and, ergo, is now 37 years old (btw: Happy belated Prime Number). Jim was born on 24th of March (month No. 3) and – guess what’s 24 – 3? Right: 21! And 24 divided by 2? ok – that’s going to become a little boring …

### 19 Responses to “73 – the best number?”

1. Craig Hastings Says:

I do agree that 73 is a very interesting number but there is something they misrepresented. 1001001 is not the binary for 73, but the binary representation of 49 which is the hex conversion of 73. Also, while they leave the leading 0 off in its representation, you can’t do that when you flip it. So 01001001 becomes 10010010. So while there are some very interesting facts provided for 73, the show did misrepresent it and Sheldon should have known this. 🙂

• feldfrei Says:

I do not know in what universe it is common practice to use leading zeros in that way for integers. You are right that the 49 is the hexadecimal representation of 73 but the binary representation of 73 is as simple as: 1*2^6 + 0*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 0*2^1 + 1*2^0 = 1*64 + 0*32 + 0*16 + 1*8 + 0*4 + 0*2 + 1 = 64 + 0 + 0 + 8 + 0 + 0 + 1 = 73.

P.S.: My date of birth (in the ddmmyyyy convention) is a 8-digit prime number (28121969). Who’s interested may calculate the probability of this coincidence.

• Ted Seeber Says:

“I do not know in what universe it is common practice to use leading zeros in that way for integers”

I think the GP was a TI-99/4A programmer at one time and learned binary-dec-hex conversions the way I did- as patterns of two-digit hexadecimal numbers representing one line of an eight-line font-based graphics set (in which you redefinend the font of ASCII characters to get high definition graphics). In 8-bit computer land, where a word is always a byte, yes, the leading zero is normative.

• descmdr Says:

Ummm… exactly why do you have to convert a decimal number into hex before converting it into binary? Sheldon is correct, period. 1001001 in base 2 is precisely 73 in base 10. There’s no reason to use base 16 as an intermediary. That’s something computer programmers do (along with prepending zeros to pad to eight digits), and Sheldon isn’t primarily a computer programmer.

• Edwin Says:

I don’t know where you went to school, but 1001001 is, indeed, the binary (base-2) representation of 73. The far-left “1” is in the 64’s place. The middle “1” is in the 8’s place, and the far-right “1” is in the 1’s place. That means that 1001001 converted to decimal (base-10) is 64+8+1 = 73.

2. blair Says:

I love The Big Bang Theory an also enjoy little numeracy games an was very pleased to read your findings from the research you have done on the number 73. I will also be boring almost every one I know with your findings so thank you 🙂

3. anthony Says:

I also noticed something else:
73 – 10 (7+3) = 63 = 3 X 21
21 = 3X7

63’s digits = 3 X 3
9 X 63 = 567
567 / 7 = 81
81’s digits = 3 X 3

567 / 3 = 189
189 / 7 = 27
27’s digits = 3 X 3
27 X 3 = 81

73 – 3 = 70
70 / (7+3) = 7

81 X 3 = 243
243’s digits = 3 X 3

7 X 7 X 7 = 343
343’s digits = 10 = 3 + 7

4. Julia Says:

oh wow… I no longer feel like a nerd 😀 I feel like I just watched another episode of The Big Bang Theory.

5. Norm Says:

It is quite simple if you bring up your Windows calculator, switch to programmer’s calculator and enter 73 in the decimal mode. Then switch to bin format and it will reveal 1001001. Duh. Also, decimal 73 in hex is 49 and 73 in octagonal is 111 another palindrome. To further elucidate but not confuse.

6. seven Says:

well, i must say with numbers you guys rock
and to sheldon cooper, hope he comes with more numbers in the next season

7. feldfrei Says:

There’s another peculiarity: Among the 21 types of vertex where regular polygons meet the one including a polygon with the largest number of edges (42) is 42-7-3. This is a nice combination of 42 and 73 (or of 37 and 42 if you order the polygons as 3-7-42). http://en.wikipedia.org/wiki/Tiling_by_regular_polygons

8. feldfrei Says:

https://feldfrei.wordpress.com/2014/01/05/funny-statistics/

• Ted Seeber Says:

And even if you are little-endian instead of big-endian, 1001001 is still 73, because 1001001 is a palindrome.

9. feldfrei Says:

How many times is “Sheldon’s best number” (73) displayed in binary on the title page of the current Max Planck Research magazine? http://www.mpg.de/8252346/MPR_2014_2

10. Kammerers kuriose Koinzidenzen | feldfrei's blog Says:

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11. hpaijmans Says:

And the best: in morse code 73 is also a palindrome: –……–
Paai