Paul's Corner

Papers

Here is small collection of my work in PDF files. Click on a title to view the content.

• Prime Numbers by Paul Underwood
• Quadratc Frobenius probable prime tests costing two selfridges
• A Restricted Domain Lucas Probable Prime Test
• Amazing Q is Negative 3 Test
• A Cubic Composite Test

Code

A parallel recursive program written in Pari/GP to factor Carmichael numbers, developed with the help of somebody nicknamed Neptune:

{CfMR(n)=e=valuation(n-1,2);nm1bye=(n-1)>>e;export(n,e,nm1bye,CFMR);vecsort(CFMR(n));}

{CFMR(N)=my(a,i,g,V=[],v,R=[]);
if(n!=N&&ispseudoprime(N),return(N),while(#R==0,
a=0;while(gcd(a,N)!=1||a%N==1,a=random(10000000)+2);a=Mod(a,N)^nm1bye;
g=lift(gcd(a-1,N));if(g>1,V=concat(V,g));
i=e;while(1,i--;g=lift(gcd(a+1,N));if(g>1,V=concat(V,g));if(i<0,break,a*=a));
V=parapply(CFMR,V);for(v=1,#V,R=concat(R,V[v]))));R;}