Code:

\\\\DSN-320-A-Pari-GP Code By Rashid Naimi 1/1/2121 >>>>>>>>>>>>>>>Error caught by Krisel. Now I have to reweight all the post dated checks for the year
primeCounter=0
compositeCounter=0
LowP=101
highP=-1
for(n=1,19^19,{\\\\\\\\\\\\\\\\\\\\\\\\\\
n1=2*n;
n2=(2+n*2)*n/2;
addend0=6;
m0=3;
addend1=(n2+1-m0)*2+addend0;
addend2=addend1+1;
p=addend1*2+1;
lowerFactor1=(p-1)/2;
upperFactor1 = lowerFactor1+1;
mLower1 = Mod(lowerFactor1,p);
mLower1 = mLower1 *lowerFactor1;
mUpper1 = Mod(upperFactor1,p);
mUpper1 = mUpper1*upperFactor1;
lowerFactor1=lowerFactor1+1;
upperFactor1 = upperFactor1-1;
primeFlag=1;
theDepth=1+2^14; \\\\\\ the larger this value, the less composites will pass the test.
if(theDepth>(p-1)/2,theDepth=(p-1)/2);
for(j=1,theDepth,
lowerFactor1=lowerFactor1-1;
upperFactor1 = upperFactor1+1;
\\mLower1 = mLower1/lowerFactor1;
iferr(mLower1 = mLower1/lowerFactor1, E, mLower1 =0;primeFlag=0;);
\\mUpper1 = mUpper1/upperFactor1;
iferr(mUpper1 = mUpper1/upperFactor1, E, mUpper1 =0;primeFlag=0;);
);
if(!primeFlag,
next(1);
,
print("\nn = ",n);
print("n1 = ",n1);
print("n2 = ",n2);
print("p = ",p," >> ", ispseudoprime(p));
print("**** ",LowP,"% < ",prcntg,"% < ",highP,"% Prime!");
);
if(!ispseudoprime(p),
if(primeFlag,
\\next(19); \\Uncomment this line to abort on 1st test failiure
);
);
if(ispseudoprime(p),primeCounter=primeCounter+1,if(primeFlag,compositeCounter=compositeCounter+1));
prcntg =round(primeCounter/(primeCounter+compositeCounter)*100);
if(prcntg < LowP,LowP=prcntg);
if(prcntg > highP,highP=prcntg);
})
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\^^^^^^^^^^^^^^^^^^

I will let you figure out why it does what it does.

I am only off by 100 years.

ETA: Hint #1: It is based on Wilson's Theorem:

https://en.wikipedia.org/wiki/Wilson%27s_theorem