67

67 is a natural number that comes after 66 and before 68. It is an odd number and is prime, meaning it has no positive divisors other than 1 and itself. In common representations, 67 is written as 67 in decimal, LXVII in Roman numerals, 1000011 in binary, and 0x43 in hexadecimal. It is the 19th prime number, a fact reflected in the prime-counting function pi(n) evaluated at 67.

In mathematics, 67 is an odd prime and has properties that are studied in elementary number theory. As a prime, it cannot be factored into smaller integers greater than 1, which makes it a basic building block in arithmetic and number theory.

Holmium is the chemical element with atomic number 67 and symbol Ho. It is a member of the lanthanide series in the periodic table. Holmium was discovered in 1878 by Per Teodor Cleve and was named after Holmia, the Latin name for Stockholm. Its compounds are valued in various technologies; holmium and holmium-doped materials are used in magnets and spectroscopy, and holmium-doped YAG lasers emit light around 2.1 micrometres. Holmium also has a high neutron absorption cross-section, which makes it useful in certain nuclear-control applications and shielding contexts.

In culture and history, the year 1967 is noted for a range of developments around the world, including influential music releases such as the Beatles’ Sgt. Pepper’s Lonely Hearts Club Band, which helped shape the era’s cultural landscape.