91

91 is a natural number that follows 90 and precedes 92. In arithmetic it is composite, since it factors as 7 multiplied by 13. This makes 91 a semiprime, the product of two distinct prime numbers. It also has notable geometric character: 91 is the 13th triangular number, because 13 × 14 divided by 2 equals 91, and it is the 7th hexagonal number, since 7 × (2×7 − 1) equals 91. In Roman numerals it is written as XCI.

In science, 91 is the atomic number of protactinium, a radioactive actinide element. Protactinium is a dense metal that occurs only in trace amounts and has several isotopes; the most long-lived natural isotope is protactinium-231, with a half-life on the order of tens of thousands of years. The element was identified in the early 20th century and has been primarily of interest for nuclear science and geochronology rather than practical applications due to its radioactivity and scarcity.

In calendar terms, 91 can denote the 91st day of the year. In common (non-leap) years this is April 1, while in leap years it falls on March 31. The number 91 also appears in basic numeral representations: it is written as XCI in Roman numerals and as 1011011 in binary.

Additional mathematical observations include that 91 is the sum of the first seven odd numbers after 1, and it sits in various number-theoretic sequences as the product of two primes that are both congruent to 1 modulo 6. As a small, versatile number, 91 serves as a convenient example of semiprimes and of numbers that are both triangular and hexagonal.