Mercer's Whiteman association brought him into contact with Hoagy Carmichael, whose `` Snowball '' Mercer relyriced as `` Lazybones '', in which form it became a hit and marked the real beginning of Mercer's song-writing career.

The Texans made themselves a comforting break on the opening kickoff when Denver's Al Carmichael was jarred loose from the ball when Dave Grayson, the speedy halfback, hit him and Guard Al Reynolds claimed it for Dallas.

Linebarger also employed the literary pseudonyms " Carmichael Smith " ( for his political thriller Atomsk ), " Anthony Bearden " ( for his poetry ) and " Felix C. Forrest " ( for the novels Ria and Carola ).

They are named for Robert Carmichael.

In this sense, Carmichael numbers are similar to prime numbers ; in fact, they are called Fermat pseudoprimes.

Carmichael numbers are sometimes also called absolute Fermat pseudoprimes.

Carmichael numbers are important because they pass the Fermat primality test but are not actually prime.

Since Carmichael numbers exist, this primality test cannot be relied upon to prove the primality of a number, although it can still be used to prove a number is composite.

Still, as numbers become larger, Carmichael numbers become very rare.

For example, there are 20, 138, 200 Carmichael numbers between 1 and 10 < sup > 21 </ sup > ( approximately one in 50 billion numbers ).< ref name =" Pinch2007 "> Richard Pinch, " The Carmichael numbers up to 10 < sup > 21 </ sup >", May 2007 .</ ref > This makes tests based on Fermat's Little Theorem slightly risky compared to others such as the Solovay-Strassen primality test.

An alternative and equivalent definition of Carmichael numbers is given by Korselt's criterion.

: Theorem ( A. Korselt 1899 ): A positive composite integer is a Carmichael number if and only if is square-free, and for all prime divisors of, it is true that ( where means that divides ).

It follows from this theorem that all Carmichael numbers are odd, since any even composite number that is square-free ( and hence has only one prime factor of two ) will have at least one odd prime factor, and thus results in an even dividing an odd, a contradiction.

( The oddness of Carmichael numbers also follows from the fact that is a Fermat witness for any even number.

From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.

Korselt was the first who observed the basic properties of Carmichael numbers, but he could not find any examples.

That 561 is a Carmichael number can be seen with Korselt's criterion.

J. Chernick proved a theorem in 1939 which can be used to construct a subset of Carmichael numbers.

The number is a Carmichael number if its three factors are all prime.

Paul Erdős heuristically argued there should be infinitely many Carmichael numbers.

In 1994 it was shown by W. R. ( Red ) Alford, Andrew Granville and Carl Pomerance that there really do exist infinitely many Carmichael numbers.

Among his numerous television roles, Carmichael guest starred with Keenan Wynn, Anthony George, and Olive Carey in the 1956 episode " Death in the Snow " of the NBC anthology series, The Joseph Cotten Show.

** James Anthony Carmichael ( producer ) & Lionel Richie ( producer & artist ) for Can't Slow Down

** James Anthony Carmichael & Lionel Richie

In 1999, BBC produced a four-part miniseries based on the novel with a screenplay written by Andrew Davies ; Wives and Daughters featuring Justine Waddell, Bill Paterson, Francesca Annis, Keeley Hawes, Rosamund Pike, Tom Hollander, Anthony Howell, Michael Gambon, Penelope Wilton, Barbara Flynn, Deborah Findlay, Iain Glen, Barbara Leigh-Hunt, and Ian Carmichael.

* Robert Anthony Carmichael Hamilton, 13th Lord Belhaven and Stenton ( born 1927 )

Session players Dan Ferguson ( guitar ) and Ron Fransen ( keyboards ) were brought in instead to play on Rarearth, which was produced by James Anthony Carmichael ( who would go onto huge success with The Commodores and Lionel Richie ) and released in 1977.

It was produced by James Anthony Carmichael and the Commodores and it was the most popular track of the album.

* Carmichael, Alexander ( 1992 ) Carmina Gadelica: Hymns and Incantations ( with illustrative notes on wards, rites, and customs dying and obsolete / orally collected in the Highlands and Islands of Scotland ) Hudson, NY, Lindisfarne Press, ISBN 0-940262-50-9

Lord Peter Wimsey was played by Ian Carmichael in a series of independent serials that ran from 1972 to 1975 and adapted five novels ( Clouds of Witness, The Unpleasantness at the Bellona Club, Five Red Herrings, Murder Must Advertise and The Nine Tailors ) and by Edward Petherbridge in 1987, in which three of the four major Wimsey / Vane novels ( Strong Poison, Have his Carcase and Gaudy Night ) were dramatised.

This is unfortunately false for weak probable primes, because there exist Carmichael numbers ; but it is true for more refined notions of probable primality, such as strong probable primes ( P = 1 / 4, Miller – Rabin algorithm ), or

Starting with a fairly conventional melancholy guitar pop sound on Lyceum and contemporaneous singles, they moved on to become more keyboard and sample / effects-based for their second and third albums, Unholy Soul and Striving For the Lazy Perfection, developing a more electronic sound, possibly as a result of their producer, Ian Carmichael, who was a member of dance band One Dove.

When Brown left the Party with Stokely Carmichael in the FBI-fomented SNCC / Panther split, Hampton assumed chairmanship of the Illinois state BPP, automatically making him a national BPP deputy chairman.

* Zoot Sims / Al Cohn-Hoagy Carmichael Sessions and More ( 1957 ) recorded in New York, Sims plays tenor and Cohn, baritone with Nick Travis, trombonist Jimmy Cleveland, pianist Elliot Lawrence, bassist Milt Hinton, and drummer Osie Johnson.

The community is served only by air, via the Aklavik / Freddie Carmichael Airport, and by winter ice road directly from Inuvik across the streams of the Mackenzie Delta.

It was really that the Lucy Carmichael / Mr. Mooney relationship continued with new names and a new setting.

* Stokely Carmichael, Trinidadian / American Black activist

During the 2008 season, he became the tenth member of the 20 / 20 Club and broke the Eagles record for games played surpassing Harold Carmichael who had 180.

# " Georgia On My Mind " ( Hoagy Carmichael / Stuart Gorrell )-2: 35

# " Georgia On My Mind " ( version 2 ) ( Hoagy Carmichael / Stuart Gorrell )-2: 37

* Aklavik ( Aklavik / Freddie Carmichael Airport, depending on demand )

Sheffer's full birth name is Mark Wayne Sheffer ; he received his nickname of Hogan from younger brother Craig, who thought he looked like pianist / composer Hoagy Carmichael.

* Bessie Carmichael / FEC K-8

* Carmichael, Alexander ( 1992 ) Carmina Gadelica: Hymns and Incantations ( with illustrative notes on wards, rites, and customs dying and obsolete / orally collected in the highlands and islands of Scotland by Alexander Carmichael ).

He played and / or recorded with Hoagy Carmichael, Count Dracula, Cab Calloway, Maynard Ferguson, Glenn Miller, Tommy Dorsey, Harry James, Fats Waller, Tony Burrello, Sarah Vaughn, Ella Fitzgerald, and Clifton Chase, mostly playing tambourine.

Abigail " Abbie " Carmichael is a fictional character on the TV drama Law & Order created by René Balcer and portrayed by model / actress Angie Harmon.

The song appears on Nat King Cole's 1960 LP " The Magic Of Christmas " ( l / k / a " The Christmas Song "), arranged by Ralph Carmichael.

Cathy Dennis ' a re-recording of the classic Patrick Adams / Greg Carmichael penned and produced " Touch Me ( All Night Long )" became a # 1 pop hit single in 1991.

In 2004, Carmichael was injured for the Supercross season, he had a knee injury ( torn ligaments / meniscus ) but came back for the Motocross season to record his second perfect season ; winning 24 of the 24 motos he raced and all 12 overalls on his Honda CRF450 ; his first effort on a 4-stroke bike.

Aklavik / Freddie Carmichael Airport is located adjacent to Aklavik, Northwest Territories, Canada.