Recursive prime p(k+1)=m*((n*p(k))^3+1)+1
Define p(0)=1; p(1)[m=2;n=2]=2*((2*p(0))^3+1)+1=19; p(2)[m=6;n=4]=6*((4*p(1))^3+1)+1=2633863; p(3)[m=14;n=1]=14*((1*2633863)^3+1)+1=14*2633863^3+15; p(4)[m=354;n=74]=354*((74*(14*2633863^3+15 ))^3+1)+1 =354*(1036*2633863^3+1110)^3+355; p(5)[m=155;n=115]=155*((115*(354*(1036*2633863^3+1110)^3+355 ))^3+1)+1 =155*(40710*(1036*2633863^3+1110)^3+40825)^3+156; p(6)[m=146;n=629]=146*((629*(155*(40710*(1036*2633863^3+1110)^3+40825)^3+156 ))^3+1)+1 =146*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+147; p(7)[m=440;n=1754]=440*((1754*(146*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+147 ))^3+1)+1 =440*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+441; p(8)[m=8385;n=185]=8385*((185*(440*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+441 ))^3+1)+1 =8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386; p(9)[m=16182;n=2988]=16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386 ))^3+1)+1; p(10)[m=79194;n=97326]=79194*((97326*(16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1))^3+1)+1; p(11)=[m=232497;n=176845]=232497*((176845*(79194*((97326*(16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1))^3+1)+1))^3+1)+1; p(11) has database ID 94439 in The List of Largest Known Primes Home Page. The direct link is HERE. These primes are recursively proven using OpenPFGW, by the command pfgw -t […]
