JBF_Interesting Numbers

Question 1

Googol

Answer 1

A googol equals 10 followed by 100 zeros, therefore, to put things into perspective, think the following number: 10,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000, or you can just be normal and think of it this way:
10^100

It is approximately 70! (Factorial). which is 70 x 69 x 68 x 67 x 66 x 65 x 64 x 63 x 62 x 61 x 60 x 59 …. x 1

To more complicate our minds, there exists a number called Googol plex, which is simply 10 to the power of Googol, written as:
10^10^100

Question 2

The number 9

Answer 2

The circle. It has 360 degrees (3 + 6 + 0 = 9)
The circle cut in half. Each half is 180 degrees (1 + 8 + 0 = 9)
The circle cut in quarters. Each quarter is 90 degrees (9 + 0 = 9)
The circle cut in 8 pieces. Each part is 45 degrees (4 + 5 + 0 = 9)
The circle cut in 16 pieces. Each part is 22.5 degrees (2 + 2 + 5 = 9)
The circle cut in 32 pieces. Each part is 11.25 degrees (1 + 1 + 2 +5 = 9)
A regular polygon inside a circle. Each angle is 60 x 3 (180 = 1 + 8 = 9)
A square. Each angle is 90 x 4 (360 = 3 + 6 + 0 = 9)

Multiplying the digits that come before 9 and summing their elements will always give us 9, examples:

9 x 1 = 9
9 x 3 = 27 = 2 + 7 = 9
9 x 7 = 63 = 6 + 3 = 9
9 x 9 = 81 = 8 + 1 = 9

Dividing the digits by 9 will always give us the same digit repeated to infinity, examples:

1 / 9 = 0.11111
3 / 9 = 0.33333
7 / 9 = 0.77777

Question 3

73

Answer 3

73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3.”’”

“In binary 73 is a palindrome, 1001001, which backwards is 1001001.”’

Question 4

Euler’s number

Answer 4

Named after Leonhard Euler, e is an irrational number and the base of the natural logarithms. Interestingly, euler’s number is known to around 1 trillion digits of accuracy [source: mathisfun.com]. It is found following this formula:

As n approaches infinity, we get a clearer vision of the value of e. When n = 100,000, e = 2.71827. An interesting property that e has, is that its slope is its value. It is also used in finance to calculate compound interest. I believe those of you who have already taken the CFA test are familiar with this information.

Question 5

The Fibonacci sequence

Answer 5

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ….

The beauty of this sequence is that it is related to nature. For example, it appears the flowering of the artichoke, some flower petals such as Daisies, honeybees, etc.. Does it even occur in the galaxy spirals?

There is even a very interesting observation based on facts that suggests that the dimensions of the Earth and Moon are in Phi relationship, forming a Triangle based on 1.618, by Gary Meisner. But what is Phi, and what is this 1.618?

If we take any two successive numbers in the sequence, their ratio (Xn / Xn-1) gets closer to 1.618 which is what we call the golden ratio:
3 / 2 = 1.5
13 / 8 = 1.666
55 / 34 = 1.61764
233 / 144 = 1.61805
…
317,811 / 196,418 = 1.61803

Question 6

23

Answer 6

Many among us have seen the movie: the number 23 which features Jim Carrey portraying the persona of Walter Sparrow as someone who becomes obssessed with the number 23 after reading about it in a book. The belief here is that this number mysteriously coincides with many events all around the world and while that can be a perfect example of Apophenia, it is still interesting to list some events that have 23 embedded in them:

The 9/11 tragic events can sum up to 23 when we write the full date as the following: 9 + 11 + 2 + 0 + 0 + 1 = 23. Of course, we could have also did 9 + 11 + 2001 = 2021.
According to the Birthday paradox, 23 is the smallest number of randomly-selected people necessary to obtain at least 50% chance of having at least two people with the same birthday. For curiousity purposes, 70 people gives us 99.99% chance.
William Shakespeare was born on April 23rd, coindidentally, he died on April 23rd as well. of course, the date of birthday is not known for sure (He was baptized on the 26th), but it is widely believed to be the 23rd of April.
The Titanic sank on April 15th, 1912. Summing the full date (including April’s number) gives us 4 + 1 + 5 + 1 + 9 + 1 + 2 = 23. Of course, this is starting to resemble data snooping and digging for patterns because we are cherry-picking the dates to sum and the ones not to sum.
The Earth is inclined on its orbital plane by 23.5 degrees. We can consider the 5 as being 2 + 3, just to make things interesting. Of course, The earth’s axis of rotation is tilted 66.5 degrees to its orbital plane, but that’s not very cool to know.
The Arecibo message consists of 1679 bits, arranged into 73 lines of 23 characters per line. This is made-up by humans of course, but it is still interesting. The Arecibo message is a message sent from earth towards space in search for intelligent life. It sums up our life.
Humans have 23 pairs of chromosomes.
The sum of the first 23 primes is 874, which is divisible by 23. Thanks, Wikipedia.
The Hiroshima bomb was dropped at 8:15. 8 + 15 = Tragic event that tore up thousands of life. Also, 8 + 15 = 23.
23 is the lowest prime that consists of consecutive digits
The Knights Templar had 23 Grand Masters.
On average, the human blood circulates through the whole body every 23 seconds.
And lastly, the ordinal number of 23 on this list is 5, amounting again to 2 + 3, but that was made-up. Bottomline here is that even though numbers are beautiful, not all of them contain some mysterious elements. I think 23 is a little overhyped considering the evidence we have. In this list, there are many other numbers with far more interesting characteristics.

Question 7

Tau (τ)

Answer 7

Tau instead which is simply τ = 2π.

Question 8

6174

Answer 8

Also known as Kaprekar’s constant, this number has a special feature if you follow the below steps (Taken from various sources, but let’s just say Wikipedia):

Take any four-digit number (at least two digits should be different).
Arrange the digits in descending and ascending order to get two new four-digit numbers.
Now, subtract the smaller number from the bigger number.
Redo step 2.
If you do this for multiple steps, you will always end up with 6174 and that is the mysterious thing about. Why do we always end up with this number no matter which numbers you start with. Let’s take an example of 2714:

7421 -1247 = 6174
Another example of 3687:

8763 -3678 = 5085;
8550 -0558 = 7992;
9972 -2799 = 7173;
7731 -1377 = 6354;
6543 -3456 = 3087;
8730 -0378 = 8352;
8532 -2358 = 6174
Now, if we have 6174, we will always stay at 6174 because 7641 -1467 = 6174.

It is also a Harshad number, meaning it is divisible by the sum of its constituents: 6174 / (6 + 1 + 7 + 4) = 6174 / 18 = 343. So, that adds to its coolness.

Question 9

13

Answer 9

number of different Archimedean solids

Question 10

17

Answer 10

“least random number” or Feller Number

sum of the first 4 prime numbers, and only prime which is the some of 4 consecutive primes

Question 11

18

Answer 11

only non-zero number that is twice the sum of its digits.

sum of the first three pentagonal numbers, making it a “pentagonal pyramidal number”

lucky number and the value for life in Jewish numerology

Question 12

21

Answer 12

smallest Fibonacci number whose digits and digit sums are also Fibonacci

Question 13

Belphegor’s prime number

Answer 13

Belphegor’s prime number is a palindromic prime number with a 666 hiding between 13 zeros and a 1 on each side. The ominous number can be abbreviated as 1 0(13) 666 0(13) 1, where the (13) denotes the number of zeros between the 1 and 666.

Although he didn’t “discover” the number, scientist and author Cliff Pickover made the sinister-looking number famous when he named it after Belphegor (or Beelphegor), one of the seven demon princes of hell in the Bible.

The number apparently even has its own devilish symbol, which looks like an upside-down symbol for pi. According to Pickover’s website(opens in new tab), the symbol is derived from a glyph in the mysterious Voynich manuscript, an early-15th-century compilation of illustrations and text that no one seems to understand.

Belphegor’s Prime is a one followed by 13 zeros, three sixes, and another 13 zeros before ending with a one. For a visual representation, that’s 1,000,000,000,000,066,600,000,000,000,001. The number is named after Belphegor, one of the seven princes of Hell. It is unique in many ways.Despite its length, Belphegor’s Prime is, not surprisingly, a prime number, which means it is only divisible by one and itself. At the same time, it is also a palindrome number, since it remains the same when read from either end. Then, it has 666, the famed number of the beast, right in its middle. If that’s not enough, it contains 31 numbers, which when read in reverse, gives “13,” which is considered an unlucky number.Belphegor’s Prime was discovered by Harvey Dubner, who had a fondness for uncovering new prime numbers. Dubner discovered the number after realizing other prime numbers could be derived from palindromic prime numbers like 16,661, if 13, 42, 506, 608, 2,472, and 2,623 zeros were added in between some numbers at either ends. In this case, 13 zeros were added between the ones and the sixes on each side. The number remained just another palindromic prime number until mathematician Cliff Pickover named it after a prince of Hell because it contained 666.

Question 14

2520

Answer 14

It is the smallest even number, divisible by all the numbers from 1 to 10. We can write 2520 as 7 × 30 × 12. It’s like

7 (number of days in a week) × 30 (number of days in a month) × 12 (number of months in a year).

Split the number 2520 as 25 and 20 and take their sum. The sum will be 25 + 20 = 45. Square of 45 is 452 = 2025 and it’s just the interchange of the numbers 25 and 20!

Question 15

73939133

Answer 15

73939133 is an interesting number as shown below

7 is prime
73 is prime
739 is prime
7393 is prime
73939 is prime
739391 is prime
7393913 is prime
73939133 is prime

Question 16

381654729

Answer 16

It’s the time for 381654729 to discuss about its speciality. See below.

First of all, it contains all the digits from 1 to 9 exactly once.
The first two digits (from the left) form a number that is divisible by 2;
The first three digits (from the left) form a number that is divisible by 3;
The first four digits (from the left) form a number that is divisible by 4;
The first five digits (from the left) form a number that is divisible by 5;
The first six digits (from the left) form a number that is divisible by 6;
The first seven digits (from the left) form a number that is divisible by 7;
The first eight digits (from the left) form a number that is divisible by 8;
The first nine digits (from the left) form a number that is divisible by 9;

Question 17

1729

Answer 17

When the British mathematician G. H. Hardy visited Indian mathematician Srinivasa Ramanujan, he commented that the number of the taxicab he rode in on was 1729 – a number he found to be rather dull. Ramanujan objected and stated it is very interesting as it is the smallest number expressible as the sum of two cubes in two different ways (1729 = 1³ + 12³ = 9³ + 10³). Such numbers are now referred to as taxicab numbers and 1729 is called the Hardy-Ramanujan number.9 = 1³ + 12³ = 9³ + 10³). Such numbers are now referred to as taxicab numbers and 1729 is called the Hardy-Ramanujan number.

Question 18

Billion

Answer 18

A billion, a one followed by nine zeros, is a thousand million. However, a little over four decades ago, the word “billion” referred to two different numbers. The first is a thousand million (a one and nine zeros), which remains a billion today, while the other is a million million (a one and 12 zeros), which we call a trillion today.This duality is due to differences between American and British English. American English has always recognized a billion as a thousand million, while British English used to recognize a billion as a million million. At the same time, British English recognized a thousand million (today’s billion) as a milliard.Likewise, there were two trillions. The first is the million million (a one and 12 zeros), which American English has always recognized as a trillion, while the other was a million million million (a one and 18 zeros), which British English recognized as a trillion. However, all these changed in 1974, when British English dumped the milliard and their definitions of billions and trillions for that of the Americans.

Question 19

5,040

Answer 19

ancient Greek philosopher Plato, who regarded it as the perfect number. 5,040 belongs to a rare group of numbers called highly composite numbers or anti-prime numbers. Unlike prime numbers, which are only divisible by one and themselves, anti-prime numbers are divisible by a lot of numbers. 5,040 is divisible by 60 numbers.Plato promoted 5,040 as the perfect number and proposed that a perfect city should not have more than 5,040 citizens. This, he thought, would allow for easy governance and division of citizens into different demographics as required.[9] To maintain this perfect number, Plato proposed that new cities should be divided into 5,040 plots and shared among 5,040 citizens. Women, children, and slaves did not count as citizens in ancient Greece, so the city’s population would have been more than 5,040.To prevent the division of a plot, whenever a citizen died, Plato suggested that an entire plot should be willed to a single preappointed son of the late citizen. The other sons were to be given to citizens who had no sons, while the daughters were to be married off. Plato also suggested that the government discourage citizens from having too many children, but when that happened, such children should be sent to another city.

Question 20

Hundred

Answer 20

The word we use for the figure above is “hundred.” However, centuries ago, the term “hundred” referred to two different numbers. The first is five scores (100), which remains today’s “hundred,” while the other was six scores (120). The disparity could be traced to Old Norse, where “hundred” was called hundrath and referred to 120.This created problems when it was introduced into English, where a “hundred” was 100. To avoid confusion, the five-score “hundred” was called the “new hundred,” “short hundred,” or “decimal hundred” (hundrath ti-raett), while the six-score “hundred” was called “old hundred,” “long hundred,” or “duodecimal hundred” (hundrath tolf-roett). However, the six-score “hundred” soon gave way to the five-score “hundred.”

Question 21

Dividing 1 by 998,001

Answer 21

998001 = 999^2

0.000001002003004005006007009010… and so on. However, the number 998 gets skipped and 999 comes exactly after 997.

What if we casually decide to divide 1 by 998,001? Surely, some of us are out there doing weird mathematical calculations, but how did we come up with this one? Interestingly, the result of this division is every set of 3-digit numbers ordered correctly up until something weird occurs. Therefore:

XXXX

Notice how the results between the zeroes tend to follow a set of ordered numbers 1, 2, 3, 4, …. 996, 997, 999. No, it was not a typo, we have literally skipped over 998 but basically wrote all the numbers between 1 and 999.

Question 22

quare of the number 111,111,111

Answer 22

12345678987654321

Question 23

1/81

Answer 23

1/81 = 0.01234567901234567901….