**241**is a prime number.

**241**has a representation as a sum of two squares:

**241**= 4

^{2}+ 15

^{2}.

**241**is the hypotenuse of a primitive Pythagorean triple:

**241**

^{2}= 120

^{2}+ 209

^{2}.

**241**is 111 in base 15.

**241**is the smallest prime

*p*such that

*p*plus the reversal of

*p*equals a palindromic prime:

**241**+ 142 = 383.

Reel Big Fish wrote a song entitled "

**241**", in which the number is repeated as the only lyric.Source: Prime Curios!

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Other properties of the number 241

241 can be represented as:

241=4^2+15^2

241=3^2+6^2+14^2

241=6^2+6^2+13^2

It can also be represented as the sum of 170 and its reverse:

241=170+071, see http://prime.utm.edu/curios

Or as rational exponents sum of eight and four:

241=(2^8+4^8+1^8)/(2^4+4^4+1^4), see http://www.archimedes-lab.org/numbers

241 also has its representation as Pythagorean triples:

241^2=29281^+50160^2

241^2+29040^2=29041^2

241 is of the form P=k*2^n+1 is therefore a Proth prime, Proth Frances discovered around 1878.

241=15*2^4+1, see http://mathworld.wolfram.com/ProthPrime

241 is a Gaussian integer, since 241=4*60+1 therefore has a representation in the unique factorization as:

241=(15+4i)(15-4i)=15^2+4^2, conjugate factorization

241=(15+4i)(4+15i)(-i), factoring symmetric with unit.

241 is a prime number with completion in January. The separability criterion for this number is that: a number is divisible by 241 if and only if

a) The sum of their scores over 217 times the units is 241 or 241K.

b) The difference between the tens and units is 24 times 0, 241 or 241K.

We demonstrate via example:

241*37=8917

a) 891+7*217=2410=241*10

b) 891-7*24=723=241*3

View http://hojamat.es/parra/divsib1.pdf

Rafael Parra Machio

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