The Bailey–Borwein–Plouffe formula (BBP formula) is a formula for . It was discovered in 1995 by Simon Plouffe and is named after the authors of the article in which it was published, David H. Bailey, Peter Borwein, and Plouffe. Before that, it had been published by Plouffe on his own site. The formula is The BBP formula gives rise to a spigot algorithm for computing the nth base-16 (hexadecimal) digit of (and therefore also the 4nth binary digit of ) without computing the preceding digits. This does not compute the nth decimal of (i.e., in base 10). But another formula discovered by Plouffe in 2022 allows extracting the nth digit of in decimal. BBP and BBP-inspired algorithms have been used in projects such as PiHex for calculating many digits of using distributed computing. The existence of this formula came as a surprise. It had been widely believed that computing the nth digit of is just as hard as computing the first n digits. Since its discovery, formulas of the general form have been discovered for many other irrational numbers , where and are polynomials with integer coefficients and is an integer base. Formulas of this form are known as BBP-type formulas. Given a number , there is no known systematic algorithm for finding appropriate , , and ; such formulas are discovered experimentally. Specializations A specialization of the general formula that has produced many results is where s, b, and m are integers, and is a sequence of integers. The P function leads to a compact notation for some solutions. For example, the original BBP formula can be written as Previously known BBP-type formulae Some of the simplest formulae of this type that were well known before BBP and for which the P function leads to a compact notation, are: (In fact, this identity holds true for a > 1: .) Plouffe was also inspired by the arctan power series of the form (the P notation can be also generalized to the case where b is not an integer): The search for new equalities Using the P function mentioned above, the simplest known formula for is for s = 1, but m > 1. Many now-discovered formulae are known for b as an exponent of 2 or 3 and m as an exponent of 2 or it some other factor-rich value, but where several of the terms of sequence A