Also can be checked in Wolfram|Alpha: https://www.wolframalpha.com/input?i=7%5E7+mod+7%21

BTW - Cool idea! Here is something very simple:

$$2^{11}-5^2 = 2023$$

In[]:= 2^11-5^2
Out[]= 2023

And thanks to John Conway's discovery of 1988 that $e^{\pi }-\pi \approx 20$ we have

$$\text{Round}\left[101 e^{\pi }-100 \pi \right]= 2023$$

In[]:= Round[101*E^Pi-100*Pi]
Out[]= 2023

I am trying to find some exact ones based on Golden Ratio, Pi, E, other irrational and transcendental numbers. Similar to Fibonacci sequence formula, but much neater than this (I hope someone will figure this out):

$$\frac{\phi ^{18}-(1-\phi) ^{18}}{\sqrt{5}}-3 \cdot 11 \cdot 17=2023$$

In[]:= FullSimplify[(GoldenRatio^18-(1-GoldenRatio)^18)/Sqrt[5]-3 11 17]
Out[]= 2023

Going into algebraic number theory

-NumberFieldDiscriminant[x /. Solve[x^3 == x^2 + 6 x + 5][[1]]]

Looks like we got another interesting postcard post by Fermat's Library on LinkedIn:

https://www.linkedin.com/feed/update/urn:li:activity:7014999420580597760

which is in Wolfram:

In[]:= (10+(9+8*7)*6)*5+4*3*2-1
Out[]= 2023

I wonder is it easy to find such combination? How many numbers we can get out of specific range using a specific set of operations? And how many combinations we have for a single number on average?

$3^2+7^2+11^2+15^2+19^2+23^2+27^2 = 2023$

If we allow concatenation.

1*2*3*456+7-8*9*10
1+2*34*5*6-7+8-9-10
1/2*345*6+78+910
12+3/4*5*67*8-9+10
12/34*5678+9+10
12+345*6-78+9+10
10-9*8-76+5*432+1
10-9*87+65*43+2-1
10*98-7*6+543*2-1
10*987/6+54/3*21 

[ (2023)^2 - 2023 ] / [6* (2023)] = 337

New year : 337 (6) + 1 = 2023 or [337 (7)* (2023)] / 2023] - 338 = 2023

Last year : 337 (6) = 2022 or 337(7) - 337 = 2022

Moving along : 337 + 1 = 338

Finding the next primes using the formula above :

[ [2023 * ( 338)* (7) - 2023] / 2023] - 338 = 2027 is prime

[ [2023 ( 338) (7) + 2023] / 2023] - 338 = 2029 is prime

[(2029+338) 2023 - 2023 / (2366)] = 2023

[(2027+338) 2023 -+2023 / (2366)] = 2023

2023 within a solution using the next twin primes