153 (one hundred [and] fifty-three) is the natural number following 152 and preceding 154.
In mathematics
The number 153 is associated with the geometric shape known as the Vesica Piscis or Mandorla. Archimedes, in his Measurement of a Circle, referred to this ratio (153/265), as constituting the "measure of the fish", this ratio being an imperfect representation of .
As a triangular number, 153 is the sum of the first 17 integers, and is also the sum of the first five positive factorials:.
The number 153 is also a hexagonal number, and a truncated triangle number, meaning that 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.
Since , it is a 3-narcissistic number, and it is also the smallest three-digit number which can be expressed as the sum of cubes of its digits. Only five other numbers can be expressed as the sum of the cubes of their digits: 0, 1, 370, 371 and 407. It is also a Friedman number, since 153 = 3 × 51.
The Biggs–Smith graph is a symmetric graph with 153 edges, all equivalent.
Another feature of the number 153 is that it is the limit of the following algorithm:
Take a random positive integer, divisible by three
Split that number into its base 10 digits
Take the sum of their cubes
Go back to the second step
An example, starting with the number 84:
There are 153 uniform polypeta that are generated from four different fundamental Coxeter groups in six-dimensional space.
In the Bible
The Gospel of John (chapter 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 have argued that 153 has some deeper significance. Jerome, for example, wrote that Oppian's Halieutica listed 153 species of fish, although this could not have been the intended meaning of the Gospel writer because Oppian composed Halieutica after the Gospel text was written, and at any rate never gave a list of fish species that clearly adds up to 153.
The number is clearly an intentional detail, given the lack of precision and detail elsewhere in the story; and theologians have lent much credence to Augustine's numerology simply because it comes from historic rather than contemporary theology.
Jerome reached much the same conclusion as Augustine that the figure is an allegorical representation of totality, but through more straightforward means rather than through numerology. In his Commentary on Ezekiel he propounded the hypothesis that 153 was meant to represent the whole universe of fish, citing as proof that contemporary poets, giving Oppian as an example, believed that there were 153 species of fish in the world. However, Robert M. Grant disproved Jerome's hypothesis by noting that Oppian actually enumerated only 149 (as catalogued by Alexander William Mair) fish species in his Halieutica (or only 152 "by adding 3 worms", in Grant's words). What Oppian actually said, moreover, was that only the gods knew the number; and other ancient authors gave different numbers that still were not 153, such as Pliny The Elder in Naturalis Historia (9.43) recording only 74, 104, or 144 (depending from how one counts, and whether one includes hard shelled animals) species of fish, and Quintus Ennius as reported by Apuleius enumerating "countless kinds of fish". "Every ancient ichthyologian counted the number of species differently." stated Grant.
David Strauss had in fact pointed out the same thing about Oppian in his Leben Jesu the century before Grant. From a strictly biological point of view, moreover, only 24 species of fish had been recorded in the Sea of Galilee by the turn of the 20th century. Theologians have continued to support Jerome's hypothesis despite Grant and Strauss, arguing variously that Jerome may have had access to other works of Oppian that are now lost, that Oppian was writing a century after the Gospel of John and at least came close, and that perhaps (despite his having mentioned Oppian by name) Jerome's reference to multiple writers actually meant other writers entirely. Grant himself opined that "there is every reason to suppose" that in fact Jerome had not actually checked Oppian's writing directly for this information, but was rather recounting secondhand some earlier Christian commentary on the Gospel of John.