In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a quartan prime is a
prime number of the form ''x''
4 + ''y''
4 where ''x'' and ''y'' are positive
integers. The
odd quartan primes are of the form 16''n'' + 1.
For example, 17 is the smallest odd quartan prime: 1
4 + 2
4 = 1 + 16 = 17.
With the exception of 2 (''x'' = ''y'' = 1), one of ''x'' and ''y'' will be odd, and the other will be
even. If both are odd or even, the resulting integer will be even, and 2 is the only even prime.
The first few quartan primes are
:
2,
17,
97,
257
__NOTOC__
Year 257 ( CCLVII) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Valerianus and Gallienus (or, less frequently, year 10 ...
,
337
__NOTOC__
Year 337 ( CCCXXXVII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Felicianus and Titianus (or, less frequently, year ...
,
641
__NOTOC__
Year 641 ( DCXLI) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. The denomination 641 for this year has been used since the early medieval period, when the Anno Domini calendar era ...
,
881
__NOTOC__
Year 881 ( DCCCLXXXI) was a common year starting on Sunday of the Julian calendar.
Events
By place Europe
* February 12 – King Charles the Fat, the third son of the late Louis the German, is crowned as Holy Roman Emper ...
, … .
See also
*
Fourth power
*
Quartic
References
*
Neil Sloane,
A Handbook of Integer Sequences', Academic Press, NY, 1973.
{{Prime number classes
Classes of prime numbers