1012

1012 is the integer following 1011 and preceding 1013. As a numeral it appears in mathematics, chronology and everyday identifiers. The entry below treats 1012 first as a number with algebraic and arithmetic properties, then as a year in historical calendars, and finally as a commonly used identifier in lists, models and codes.

Mathematical properties

In arithmetic 1012 is an even composite number. Its prime factorization is 2²·11·23. From this factorization one can derive a number of standard invariants and representations:

• Divisors: 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012.
• Sum of all divisors σ(1012) = 2016; sum of proper divisors = 1004, so 1012 is a deficient number.
• Euler's totient φ(1012) = 440.
• Binary: 1111110100; hexadecimal: 0x3F4; Roman numerals: MXII.
• With eight 1 bits in its binary expansion, 1012 is classified among the so-called "evil" numbers (numbers with an even number of 1s in binary).

Calendar years (AD and BC)

As a year number, AD 1012 denotes a year in the early medieval period under the Julian calendar; because the Julian calendar treated every fourth year as a leap year, AD 1012 was a leap year. AD 1012 falls within the general era often described as the High Middle Ages or the later phase of the early Middle Ages in Europe, the middle period of the Heian era in Japan, and the Song dynasty in China. The year 1012 BC refers to a different era entirely, situated in the late second millennium BCE; specific events attributed to that century are treated within the frameworks of Near Eastern, Aegean and other regional chronologies.

Uses and cultural notes

Numbers like 1012 commonly serve as model numbers, street addresses, product identifiers, catalogue entries and episode or flight numbers. They also appear in technical contexts such as port numbers, file names or parts lists. Because 1012 is concise and easy to read in multiple numeral systems, it is convenient for labelling and indexing.

Though not remarkable in the way a prime or a round power of ten is, 1012 exemplifies typical behavior of a four-digit composite: it has multiple nontrivial divisors, a nontrivial totient, and straightforward digital and positional representations useful across mathematics and everyday numbering systems.