41
41 is a prime number, the atomic number of niobium, and forms a twin-prime pair with 43.
- Odd
- Prime
Where 41 fits
Why 41 is special
41 and 43 are two of the closer twin-prime pairs in the 0-100 range, sitting either side of the highly composite 42.
Same number, different meanings
How 41 is understood across different contexts — never implying one meaning because of another.
- Mathematics
41 and 43 are two of the closer twin-prime pairs in the 0-100 range, sitting either side of the highly composite 42.
- Technology & computing
Almost every MRI scanner in the world runs on element 41. Niobium-titanium alloy superconducts at liquid-helium temperatures and, unlike most superconductors, can be drawn into a ductile wire and wound into a magnet, which is what makes a stable multi-tesla field practical to build. The same wire is used in the Large Hadron Collider's main dipole magnets.
- Geography
+41 reaches Switzerland, at the start of the 4x block the ITU allocated to central and western Europe alongside +43 Austria, +44 the United Kingdom and +49 Germany. Switzerland's own emergency numbers are 117, 118 and 144 rather than a single line, though 112 works alongside them as it does across Europe.
- Science
41 is the atomic number of niobium. Alloyed with titanium it superconducts at practical temperatures, which is what makes the powerful magnets inside MRI scanners possible.
41 is part of
Factors & digit properties
- Divisors (2)
- 1, 41
- Prime factorisation
- 41
- Digit sum
- 5
- Digital root
- 5
Representations
- Decimal
- 41
- Scientific notation
- 4.100 × 10^1
Roman numerals
X L I
XLI uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 0 1 0 0 1
1 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 41
Octal
5 1
5 × 8 + 1 × 1 = 41
Hexadecimal
2 9
2 × 16 + 9 × 1 = 41
Read as powers of two: 32 + 8 + 1 = 41.
In historical numeral systems
Egyptian
4 hobbles, 1 stroke
4 × 10 + 1 × 1 = 41. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
4 corner wedges + 1 vertical wedge
41 fits in a single sexagesimal place: 4 corner wedges + 1 vertical wedge.
Greek (Ionic)
mu, then alpha, marked as a numeral
mu-alpha + keraia
mu + alpha written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
mem, then alef
mem-alef
mem (40) + alef (1) = 41, written in descending order.
Chinese numerals
sì shí yī
sì shí yī
四 before 十 multiplies it: 4 tens. 一 after it adds 1. The written form mirrors the arithmetic — "sì shí yī". The financial (anti-fraud) form is 肆拾壹.
Maya
2 dots (upper, twenties place) over 1 dot (lower, units place)
2 × 20 + 1 = 41. Places stack vertically with the smallest at the bottom, so the upper group is worth twenty times the lower.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Deficient number
- Sophie Germain prime
- Twin prime
Related numbers & connections
41 is a factor of 82 (41 × 2 = 82).
View 82 →41 and 43 are twin primes — two primes exactly two apart.
View 43 →Switzerland's ISO numeric code and calling code. Its adjacency to Sweden in one system and not the other is a reminder that both orderings are conventions.
View 756 →Technology & computing
Almost every MRI scanner in the world runs on element 41. Niobium-titanium alloy superconducts at liquid-helium temperatures and, unlike most superconductors, can be drawn into a ductile wire and wound into a magnet, which is what makes a stable multi-tesla field practical to build. The same wire is used in the Large Hadron Collider's main dipole magnets.
DocumentedTechnology & computing
Geography
+41 reaches Switzerland, at the start of the 4x block the ITU allocated to central and western Europe alongside +43 Austria, +44 the United Kingdom and +49 Germany. Switzerland's own emergency numbers are 117, 118 and 144 rather than a single line, though 112 works alongside them as it does across Europe.
DocumentedGeographyGeography: Switzerland
Mathematics
Euler noticed in 1772 that the expression n² + n + 41 returns a prime for every whole number n from zero to thirty-nine — forty primes in a row from a formula that fits on one line. It fails at forty, where the answer is 41 squared, and Euler also proved that no polynomial can generate primes forever. The unusual length of the run is a consequence of a genuine property of 41 in the theory of imaginary quadratic fields, not a coincidence.
DocumentedMathematicsPeriod: 177241 is prime, and forms a twin-prime pair with 43 — two primes exactly two apart.
DocumentedMathematics
Science
41 is the atomic number of niobium. Alloyed with titanium it superconducts at practical temperatures, which is what makes the powerful magnets inside MRI scanners possible.
DocumentedScience
Common questions
What is Euler's prime-generating formula?
n² + n + 41 gives a prime for every whole number n from 0 to 39 — forty primes from one line of arithmetic. Euler noticed it in 1772. It breaks at n = 40, where the answer is 41², and no polynomial can produce primes forever. The unusually long run is a consequence of a genuine property of 41, not a coincidence.
Is 41 a prime number?
Yes, 41 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 41?
The factors of 41 are 1, 41.
What is 41 in Roman numerals?
41 in Roman numerals is XLI. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be XXXXI, which Roman inscriptions used freely — the strict subtractive form is a later convention.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 5 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026