A number that is not fun

[Neil Sloane]

There is a new German video on Youtube based on the OEIS: 

Quarks Dimension Ralph: Die Zahl, die garantiert keinen Spaß macht

(The number that is guaranteed not to be fun)

https://www.youtube.com/watch?v=oJ_I-nAB5Yw

English summary:

Do you have a favorite number? Perhaps 7, because it’s considered lucky? Or 42, because it’s supposed to be the answer to everything? So, are numbers not quite as neutral as one might expect? How is even the most seemingly objective science influenced by our human preferences?

Some numbers stand out. But have you ever wondered which number is the most boring?

In the 1960s, mathematician Neil Sloane began collecting sequences of numbers—such as natural numbers, prime numbers, or the Fibonacci sequence. This eventually grew into a massive database: the OEIS, or Online Encyclopedia of Integer Sequences—a sort of Wikipedia for numbers.

Computer scientist Philippe Guglielmetti used this very database in his quest to find the world's most boring number. He analyzed how frequently individual numbers appear in the OEIS, revealing a surprising gap between numbers that appear very often and those that appear much more rarely.

People are particularly interested in prime numbers, square numbers, and numbers with striking patterns. And since humans decide which sequences are collected and studied, our preferences shape which numbers are deemed interesting.

Ultimately, Ralph settles on a number that does not appear in any of the sequences stored in the OEIS. It is the smallest known "most boring" number—and Ralph’s current favorite "diss."

This episode of *Quarks Dimension Ralph* shows why even boring numbers can be interesting, and what this reveals about mathematics and the merely apparent objectivity of science.

[Seiichi Manyama]

Dear all,

Thanks for sharing this.

For reference, I maintain a page on my site that uses data from the OEIS repository to track and regularly update the current top 50 uninteresting numbers:

https://manman4.github.io/

Seiichi

2026年6月25日(木) 20:32 Neil Sloane <njas...@gmail.com>:

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[Tom Duff]

Of course, all positive integers appear in A27, so there are no boring numbers.

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[Ruud H.G. van Tol]

Indeed, so maybe call them shy numbers in stead.

-- Ruud

On 2026-06-25 16:11, Tom Duff wrote:
> Of course, all positive integers appear in A27, so there are no
boring numbers.

[...]

[Geoffrey Caveney]

Neil and Ralph,

For a given prime number p, consider the square number 4*(p^2). (For p>=3, this is the smallest even square number that has prime factor p.)

Find the smallest integer that has 

(1) a prime factor with nearest square number 4*(p^2), and

(2) an even residue (0, 2, 4, ...) modulo every prime <= p.

For p=2, the smallest such integer is 26. Its prime factor 13 has nearest square number 16 = 4*(2^2), and 26 == 0 mod 2.

For p=3, the smallest such integer is 62. Its prime factor 31 has nearest square number 36 = 4*(3^2), and 62 == 0 mod 2 and == 2 mod 3.

For p=5, the smallest such integer is 194. Its prime factor 97 has nearest square number 100 = 4*(5^2), and 194 == 0 mod 2 ; == 2 mod 3 ; and == 4 mod 5.

Now let us skip ahead to consider p = 23 :

For p=23, the smallest such integer is the "boring number" 20990.

Its prime factor 2099 has nearest square number 2116 = 4*(23^2), and 

20990 == 0 mod 2 ;

== 2 mod 3 ;

== 0 mod 5 ;

== 4 mod 7 ; 

== 2 mod 11 ;

== 8 mod 13 ;

== 12 mod 17 ;

== 14 mod 19 ; and

== 14 mod 23.

There is no smaller integer with a prime factor between 2070 and 2162 (such that its nearest square number is 2116) that has this property of an even residue modulo every prime number <= 23.

Geoffrey

--

[Hugo Pfoertner]

If there is already such a nice explanation for 20990, perhaps there is also one for the smallest prime number not found in DATA, 48973?

[Geoffrey Caveney]

Hugo,

Sequence https://oeis.org/A096376 cites the paper https://arxiv.org/pdf/2512.06980 published just last year, which on pp. 9-10 establishes that the graphical Stirling numbers B(M(St_n); 2n) = 2n^2 - 3n + 3 align with sequence A096376 when adjusted for indexing. (The simplest formula for A096376 is 2n^2 + n + 2.) The sequence begins 2, 5, 12, 23, 38, 57, 80, 107, 138, 173, .... 

[It appears that the paper excludes the initial 2 from this sequence for technical reasons related to Mycielskian star graph Bell numbers.]

The prime number 48973 can be expressed as 138^2 + 173^2, the sum of the squares of two consecutive graphical Stirling numbers of the form B(M(St_n); 2n) = 2n^2 - 3n + 3 : 

2*81 - 3*9 + 3 = 138 and 

2*100 - 3*10 + 3 = 173

The sequence of sums of squares of two consecutive graphical Stirling numbers of the form B(M(St_n); 2n) begins with these terms :

[following the paper in excluding the initial 2 from the list of these graphical Stirling numbers]

5^2 + 12^2 = 169

12^2 + 23^2 = 673

23^2 + 38^2 = 1973

38^2 + 57^2 = 4693

57^2 + 80^2 = 9649

80^2 + 107^2 = 17849

107^2 + 138^2 = 30493

138^2 + 173^2 = 48973

...

Alternatively, we may describe this sequence as numbers of the form 8*n^4 - 8*n^3 + 30*n^2 - 14*n + 13, which is the expansion of (2n^2 + n + 2)^2 + (2n^2 - 3n + 3)^2.

Geoffrey

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[Amarnath Krishnamurthy]

By being the  most boring number it stands out as an interesting number. A paradox 

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[M. F. Hasler]

On Sat, Jun 27, 2026, 13:23 Hugo Pfoertner <> wrote:

If there is already such a nice explanation for 20990, perhaps there is also one for the smallest prime number not found in DATA, 48973?

Geoffrey Caveney <> wrote (to me):

It seems more difficult to find an interesting property of the next "boring number" in line, 23543.

 

23543 is an odd semiprime = 13 * 1811. These two prime factors share the following property:...

Geoffrey went on explaining the property that seemed a bit complicated to me (involving the greater of the smallest pair of consecutive primes with gap 2n -2 + 2*ceiling(n/2) and both adjacent gaps 2n + 2*ceiling(n/2)). 

I noticed a simpler (albeit "base") one:

They are reflectable emirps (A007628 - the same upside-down, and also prime when read from left to right).

23543 is the 15th such semiprime (i.e., product of p, q in A007628), the first ones are : 

169, 403, 961, 1469, 3503, 4043, 9641, 12769, 13403, 13429, 14339, 15353, 16913, 17953, 23543, ...

So I proposed this as oeis.org/draft/A397254.

- Maximilian