Magata's constant is the sum of the coefficients in Newton's divided difference interpolation formula for the sequence of prime
numbers. For 
,
let the Lagrange interpolating polynomial
through 
for 
,
where 
is the 
th
prime number, be
 |
(1)
|
where the empty product for 
is 1. For the first few points, the polynomials
are
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
So the first few values of 
, 
, 
, ..., are 2, 1, 1/2, 
, 1/8, 
, ... (OEIS A118210
and A118211).
Now consider the partial sums of these coefficients, namely 2, 3, 7/2, 10/3, 83/24, 203/60, 2459/720, ... (OEIS A118203 and A118204). As first noted by F. Magata in 1998, the sum appears to converge to the value 3.407069... (OEIS A092894), now known as Magata's constant.
