Bignum Bakeoff

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The Bignum Bakeoff was a programming contest held by David Moews in December 2001. The object of the competition is to write a C program with at most 512 characters (ignoring whitespace) that returns the largest possible number, assuming a computer with infinite resources. The entries were graded relative to the fast-growing hierarchy.

A total of twenty entries (plus one entry which was post-mortem) were submitted by various people (nine of them from the same person), and fifteen (including post-mortem entry) of the programs outputted a large number (the other six either did not terminate or outputted -1). The entry that came in second place was marxen.c by Heiner Marxen, which uses a variant of Goodstein sequences, and the winning entry was loader.c by Ralph Loader, which diagonalizes over the calculus of constructions. The output of loader.c is in fact one of the largest numbers known, and it has been nicknamed Loader's number.

This YouTube playlist runs through some of the main ideas used by contestants with a particular focus on the mathematics behind marxen.c and loader.c.

List of entries by output size

• carnahan.c, pete.c, pete-2.c - did not terminate
• dovey.c, edelson.c, f.c - outputted -1 due to failed attempts to output the largest number
• pete-3.c = 9*2^1566
• pete-9.c ~ 2↑↑386,201,107
• pete-8.c ~ 2↑↑386,201,107
• harper.c ~ 2↑↑(10^1030,102,999)
• ioannis.c ~ f_ω+1(115)
• goldstoner.c ~ f_ω+2(199) (post-mortem entry)
• chan-2.c ~ f_ω+47(10³⁹)
• chan-3.c ~ f_ω2+4(199,999)
• pete-4.c ~ f_ω33(100,000)
• chan.c ~ f_ω50(100,000)
• pete-5.c ~ f_ω¹¹+16(1000)
• pete-6.c ~ f_ω²³(10³⁰¹¹)
• pete-7.c ~ f_ω^ω(2↑↑35)
• marxen.c ~ f_ε0+ω³(1,000,000)
• loader.c = D⁵(99)

Specific numbers

• 99,999,999 is the largest eight-digit number in decimal, being equal to \(10^8 - 1\). For this reason, it has been used in harper.c.
  • It is also the largest number not causing an integer overflow on standard four-function calculators.
  • Furthermore, it is the price of the upgrade “Coconut cookies” (in cookies) in the game Cookie Clicker.
• 999,999,999,999,999,999,999,999,999,999,999,999,999 is the largest 39-digit number in decimal. For this reason, it has been used in chan-2.c.
  • It's prime factorization is 3³ × 37 × 53 × 79 × 265,371,653 × 900,900,900,900,990,990,990,991.
  • Furthermore, it is the price of the upgrade “Royal raspberry chocolate butter biscuit” (in cookies) in the game Cookie Clicker.

External links

• David Moews' website

Large numbers in computers

Main article: Numbers in computer arithmetic

127 · 128 · 256 · 32767 · 32768 · 65536 · 2147483647 · 4294967296 · 9007199254740991 · 9223372036854775807 · FRACTRAN catalogue numbers
Bignum Bakeoff contestants: pete-3.c · pete-9.c · pete-8.c · harper.c · ioannis.c · chan-2.c · chan-3.c · pete-4.c · chan.c · pete-5.c · pete-6.c · pete-7.c · marxen.c · loader.c
Channel systems: lossy channel system · priority channel system
Concepts: Recursion