153 (number): Map

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153
Ordinal 153
Cardinal 153rd
Factorization 153 = 3^2 \cdot 17
Divisors 1, 3, 9, 17, 51, 153
Roman numeral CLIII
Binary 10011001
Octal 231

One hundred (and) fifty-three is the natural number following one hundred fifty-two and preceding one hundred fifty-four.

As a triangular number, it is the sum of the first 17 integers, and also the sum of the first five positive factorials. It is also a hexagonal number. It is also one of six known truncated triangle numbers, meaning 1, 15, and 153 are all triangle numbers

The distinct prime factors of 153 add up to 20, and so do the ones of 154, hence the two form a Ruth-Aaron pair.

Another interesting feature of the number 153 is that it's the limit of the following algorithm:

1. Take a random positive integer, divisible by three.
2. Split that number into its base 10 digits.
3. Take the sum of their cubes.
4. Go to the second step.

An example, starting with the number 84:

\begin{align}8^3 + 4^3 &=& 512 + 64 &=& 576\\5^3 + 7^3 + 6^3 &=& 125 + 343 + 216 &=& 684\\6^3 + 8^3 + 4^3 &=& 216 + 512 + 64 &=& 792\\7^3 + 9^3 + 2^3 &=& 343 + 729 + 8 &=& 1080\\1^3 + 0^3 + 8^3 + 0^3 &=& 1 + 0 + 512 + 0 &=& 513\\5^3 + 1^3 + 3^3 &=& 125 + 1 + 27 &=& 153\\1^3 + 5^3 + 3^3 &=& 1 + 125 + 27 &=& 153\end{align}

Evagrius Ponticus considered 153 to represent a harmonization of contrasts, since 153 = 100 + 28 + 25, with 100 a square, 28 a triangle and 25 a circle.

Since 153 = 1^3 + 5^3 + 3^3, it is a 3-narcissistic number, and it is a Friedman number since 153 = 3 * 51. It is a Harshad number in base 10.

153 can also be written as 1!+2!+3!+4!+5!.

In the Bible

The Gospel of John (21:1-14) includes the narrative of the Miraculous catch of 153 fish as the third appearance of Jesus after his resurrection.. The precision of the number of fish in this narrative has long been considered peculiar, and many scholars, throughout history, have argued that 153 has some deeper significance. Jerome, for example, wrote that Oppian's Halieutica listed 153 species of fish. St. Louis-Marie de Montfort, in his fifth method of saying the Rosary, considers that the number 153 was foreshadowing of the number of Hail Marys in the Rosary:"its fruitfulness as shown in the net that St. Peter by order of Our Lord threw into the sea and which though filled with 153 [representing 153 Hail Marys in the Rosary] fish did not break." [54084]

The fact that the measure of the fish was known to include 153, as one of its two numbers, and that the measure of how many fish the disciples are said to have caught is also 153, has not gone unnoticed by many scholars , with some suggesting that the number of fish in the New Testament episode is simply down to being the most familiar large number to the writer, or a deliberate reference to the geometric nomenclature as a sort of in-joke. A story was told of Pythagoras by Iamblichus, then Porphyry describing how Pythagoras correctly predicted the amount of fish caught by fishermen. Neither Iamblichus or Porphyry's accounts describe a miraculous catch nor specify the number of fish caught and the Gospel accounts make no mention of Jesus predicting the number of fish caught. Some scholars have argued that the entire Biblical episode is a coded reference to a geometric diagram, since Pythagoreanism saw geometry and numbers as having deep esoteric meaning, and via Hermeticism (and more minor routes) it was profoundly influential in the development of Hellenic mystery religion, and in certain aspects of gnosticism, an early belief system with disputed origins. The number 153 has several curious mathematical properties.

Scholars regarding the unnamed Beloved Disciple as Mary Magdalene have noted that in Greek gematria her epithet "η Μαγδαληνή" (h Magdalhnh) bears the number 153, thus revealing the identity of the Gospel's author.

In other fields

153 is also:

153 is equal to the sum of the cubes of its digits:1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153.

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 140 - 141