Prime Generating Quadratic Polynomials

Today I turned 25919 days old, a prime day as I like to call days of this type, because 25919 is a prime number. Now one of its properties is that it is a member of OEIS A117081:

A117081

\(a(n) = 36 \,n^2 - 810 \,n + 2753\), producing the conjectured record number of 45 primes in a contiguous range of \(n\) for quadratic polynomials, i.e., |\(a(n\)| is prime for \(0 \leq n < 44\).

So the quadratic polynomial is:$$36x^2-810x+2753$$25919 is one of those 45 primes, corresponding to \(x=39\). Here is the list of all 45 primes (with 25919 highlighted in bold):

2753, 1979, 1277, 647, 89, -397, -811, -1153, -1423, -1621, -1747, -1801, -1783, -1693, -1531, -1297, -991, -613, -163, 359, 953, 1619, 2357, 3167, 4049, 5003, 6029, 7127, 8297, 9539, 10853, 12239, 13697, 15227, 16829, 18503, 20249, 22067, 23957, 25919, 27953, 30059, 32237, 34487, 36809

Back in 2018, I posted about Prime Producing Linear Polynomials and now this got me thinking about prime generating quadratic polynomials. SageMathCell makes it easy to investigate these types of polynomials. Figure 1 shows the code that I set up (permalink) for the particularly interesting polynomial:$$2x^2-108x+1259$$

Figure 1

This polynomial produces an impressive 92 primes out of a 100 but only 66 of them are distinct. I found it and others using this online source (see Figure 2 for screenshot).

Figure 2

However, the record of 95 primes out of a 100 is held by this polynomial:$$x^2-69x+1231$$It is related to Euler's polynomial \(x^2+x+41\) by the substitution \(n=m-35\). Anyway, today is special in that it's not only a prime day but the prime under review (25919) is one of a conjectured 45 maximum possible primes produced in a contiguous range of input values for a quadratic polynomial.