{"id":109,"date":"2010-04-29T13:20:28","date_gmt":"2010-04-29T17:20:28","guid":{"rendered":"http:\/\/bitc.bme.emory.edu\/~lzhou\/blogs\/?p=109"},"modified":"2010-05-04T18:05:20","modified_gmt":"2010-05-04T22:05:20","slug":"new-prime-found-2","status":"publish","type":"post","link":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/?p=109","title":{"rendered":"New Prime Found"},"content":{"rendered":"<p>18762*2*(41968149*2^23209+1)*(97254741*2^21701+1)*(12450795*2^11213+1)*(20092671*2^11213+1)*(28115529*2^11213+1)*(43998375*2^11213+1)*(99539031*2^11213+1)*(14024781*2^9941+1)*(26534229*2^9941+1)*(78981231*2^9689+1)*(57506259*2^96<br \/>\n89+1)*(24975705*2^9689+1)*(7770399*2^9689+1)*(99738639*2^4423+1)*(97478625*2^4423+1)*(96783729*2^4423+1)*(86445039*2^4423+1)*(86022459*2^4423+1)*(82860819*2^4423+1)*(82852119*2^4423+1)*(54983739*2^4423+1)*(37753119*2^4423+1)*(264<br \/>\n48255*2^4423+1)*(26055441*2^4423+1)*(24439281*2^4423+1)*(22820631*2^4423+1)*(17436999*2^4423+1)*(14395845*2^4423+1)*(12058929*2^4423+1)*(7288671*2^4423+1)*(96317565*2^4253+1)*(82195221*2^4253+1)*(77293269*2^4253+1)*(71596305*2^42<br \/>\n53+1)*(57309375*2^4253+1)*(56921445*2^4253+1)*(34719825*2^4253+1)*(16894545*2^4253+1)*(1792431*2^4253+1)*(97688691*2^3217+1)*(91257465*2^3217+1)*(91090419*2^3217+1)*(86093541*2^3217+1)*(85877469*2^3217+1)*(84069831*2^3217+1)*(795<br \/>\n33441*2^3217+1)*(78684369*2^3217+1)*(76317555*2^3217+1)*(76037751*2^3217+1)*(72552339*2^3217+1)*(68274339*2^3217+1)*(58155531*2^3217+1)*(53160021*2^3217+1)*(48317421*2^3217+1)*(44497059*2^3217+1)*(42114315*2^3217+1)*(41096715*2^3<br \/>\n217+1)*(39648561*2^3217+1)*(39327861*2^3217+1)*(34314159*2^3217+1)*(29652849*2^3217+1)*(24763389*2^3217+1)*(24430989*2^3217+1)*(23748699*2^3217+1)*(20007255*2^3217+1)*(18596781*2^3217+1)*(13656495*2^3217+1)*(11109435*2^3217+1)*(8<br \/>\n869755*2^3217+1)*(6894645*2^3217+1)*(5209209*2^3217+1)*(2851731*2^3217+1)*(96288201*2^2281+1)*(95937261*2^2281+1)*(95933985*2^2281+1)*(94364775*2^2281+1)*(92893239*2^2281+1)*(92748381*2^2281+1)*(90589905*2^2281+1)*(87734841*2^228<br \/>\n1+1)*(86566965*2^2281+1)*(86258499*2^2281+1)*(85734651*2^2281+1)*(84715839*2^2281+1)*(81532725*2^2281+1)*(79884849*2^2281+1)*(79081275*2^2281+1)*(76694835*2^2281+1)*(72081945*2^2281+1)*(72017001*2^2281+1)*(71253915*2^2281+1)*(688<br \/>\n93959*2^2281+1)*(68085225*2^2281+1)*(65410995*2^2281+1)*(63626145*2^2281+1)*(60039321*2^2281+1)*(56002311*2^2281+1)*(54061581*2^2281+1)*(53434575*2^2281+1)*(49409151*2^2281+1)*(41855025*2^2281+1)*(40910079*2^2281+1)*(40303905*2^2<br \/>\n281+1)*(40129041*2^2281+1)*(40018299*2^2281+1)*(31393209*2^2281+1)*(30810039*2^2281+1)*(27754761*2^2281+1)*(22185849*2^2281+1)*(20176311*2^2281+1)*(16289589*2^2281+1)*(14164635*2^2281+1)*(14147229*2^2281+1)*(11236485*2^2281+1)*(1<br \/>\n0213875*2^2281+1)*(4128945*2^2281+1)*(4039659*2^2281+1)*(4018065*2^2281+1)*(3928155*2^2281+1)*(3015531*2^2281+1)*(98028735*2^2203+1)*(97108935*2^2203+1)*(96046179*2^2203+1)*(95560221*2^2203+1)*(94884285*2^2203+1)*(94506579*2^2203<br \/>\n+1)*(91113195*2^2203+1)*(89055891*2^2203+1)*(88513845*2^2203+1)*(88293609*2^2203+1)*(87081549*2^2203+1)*(84254751*2^2203+1)*(78451869*2^2203+1)*(77693889*2^2203+1)*(76733511*2^2203+1)*(76650939*2^2203+1)*(76129479*2^2203+1)*(7458<br \/>\n5799*2^2203+1)+1<\/p>\n<p>Proof:<br \/>\n$ more cp1.cert<br \/>\n$ .\/pfgw -t -h&#8221;helper&#8221; cp1<br \/>\nPFGW Version 3.3.2.20100216.x86_Dev [GWNUM 25.13]<\/p>\n<p>Resuming input file cp1 at line 2<\/p>\n<p>Primality testing<br \/>\n18762*2*(41968149*2^23209+1)*(97254741*2^21701+1)*(12450795*2^11213+1)*(20092671*2^11213+1)*(28115529*2^11213+1)*(43998375*2^11213+1)*(99539031*2^11213+1)*(14024781*2^9941+1)*(26534229*2^9941+1)*(78981231*2^9689+1)*(57506259*2^96<br \/>\n89+1)*(24975705*2^9689+1)*(7770399*2^9689+1)*(99738639*2^4423+1)*(97478625*2^4423+1)*(96783729*2^4423+1)*(86445039*2^4423+1)*(86022459*2^4423+1)*(82860819*2^4423+1)*(82852119*2^4423+1)*(54983739*2^4423+1)*(37753119*2^4423+1)*(264<br \/>\n48255*2^4423+1)*(26055441*2^4423+1)*(24439281*2^4423+1)*(22820631*2^4423+1)*(17436999*2^4423+1)*(14395845*2^4423+1)*(12058929*2^4423+1)*(7288671*2^4423+1)*(96317565*2^4253+1)*(82195221*2^4253+1)*(77293269*2^4253+1)*(71596305*2^42<br \/>\n53+1)*(57309375*2^4253+1)*(56921445*2^4253+1)*(34719825*2^4253+1)*(16894545*2^4253+1)*(1792431*2^4253+1)*(97688691*2^3217+1)*(91257465*2^3217+1)*(91090419*2^3217+1)*(86093541*2^3217+1)*(85877469*2^3217+1)*(84069831*2^3217+1)*(795<br \/>\n33441*2^3217+1)*(78684369*2^3217+1)*(76317555*2^3217+1)*(76037751*2^3217+1)*(72552339*2^3217+1)*(68274339*2^3217+1)*(58155531*2^3217+1)*(53160021*2^3217+1)*(48317421*2^3217+1)*(44497059*2^3217+1)*(42114315*2^3217+1)*(41096715*2^3<br \/>\n217+1)*(39648561*2^3217+1)*(39327861*2^3217+1)*(34314159*2^3217+1)*(29652849*2^3217+1)*(24763389*2^3217+1)*(24430989*2^3217+1)*(23748699*2^3217+1)*(20007255*2^3217+1)*(18596781*2^3217+1)*(13656495*2^3217+1)*(11109435*2^3217+1)*(8<br \/>\n869755*2^3217+1)*(6894645*2^3217+1)*(5209209*2^3217+1)*(2851731*2^3217+1)*(96288201*2^2281+1)*(95937261*2^2281+1)*(95933985*2^2281+1)*(94364775*2^2281+1)*(92893239*2^2281+1)*(92748381*2^2281+1)*(90589905*2^2281+1)*(87734841*2^228<br \/>\n1+1)*(86566965*2^2281+1)*(86258499*2^2281+1)*(85734651*2^2281+1)*(84715839*2^2281+1)*(81532725*2^2281+1)*(79884849*2^2281+1)*(79081275*2^2281+1)*(76694835*2^2281+1)*(72081945*2^2281+1)*(72017001*2^2281+1)*(71253915*2^2281+1)*(688<br \/>\n93959*2^2281+1)*(68085225*2^2281+1)*(65410995*2^2281+1)*(63626145*2^2281+1)*(60039321*2^2281+1)*(56002311*2^2281+1)*(54061581*2^2281+1)*(53434575*2^2281+1)*(49409151*2^2281+1)*(41855025*2^2281+1)*(40910079*2^2281+1)*(40303905*2^2<br \/>\n281+1)*(40129041*2^2281+1)*(40018299*2^2281+1)*(31393209*2^2281+1)*(30810039*2^2281+1)*(27754761*2^2281+1)*(22185849*2^2281+1)*(20176311*2^2281+1)*(16289589*2^2281+1)*(14164635*2^2281+1)*(14147229*2^2281+1)*(11236485*2^2281+1)*(1<br \/>\n0213875*2^2281+1)*(4128945*2^2281+1)*(4039659*2^2281+1)*(4018065*2^2281+1)*(3928155*2^2281+1)*(3015531*2^2281+1)*(98028735*2^2203+1)*(97108935*2^2203+1)*(96046179*2^2203+1)*(95560221*2^2203+1)*(94884285*2^2203+1)*(94506579*2^2203<br \/>\n+1)*(91113195*2^2203+1)*(89055891*2^2203+1)*(88513845*2^2203+1)*(88293609*2^2203+1)*(87081549*2^2203+1)*(84254751*2^2203+1)*(78451869*2^2203+1)*(77693889*2^2203+1)*(76733511*2^2203+1)*(76650939*2^2203+1)*(76129479*2^2203+1)*(7458<br \/>\n5799*2^2203+1)+1<br \/>\n[N-1, Brillhart-Lehmer-Selfridge]<br \/>\nReading factors from helper file helper<br \/>\nRunning N-1 test using base 2<br \/>\nCalling Brillhart-Lehmer-Selfridge with factored part 33.42%<br \/>\n18762*2*(41968149*2^23209+1)*(97254741*2^21701+1)*(12450795*2^11213+1)*(20092671*2^11213+1)*(28115529*2^11213+1)*(43998375*2^11213+1)*(99539031*2^11213+1)*(14024781*2^9941+1)*(26534229*2^9941+1)*(78981231*2^9689+1)*(57506259*2^96<br \/>\n89+1)*(24975705*2^9689+1)*(7770399*2^9689+1)*(99738639*2^4423+1)*(97478625*2^4423+1)*(96783729*2^4423+1)*(86445039*2^4423+1)*(86022459*2^4423+1)*(82860819*2^4423+1)*(82852119*2^4423+1)*(54983739*2^4423+1)*(37753119*2^4423+1)*(264<br \/>\n48255*2^4423+1)*(26055441*2^4423+1)*(24439281*2^4423+1)*(22820631*2^4423+1)*(17436999*2^4423+1)*(14395845*2^4423+1)*(12058929*2^4423+1)*(7288671*2^4423+1)*(96317565*2^4253+1)*(82195221*2^4253+1)*(77293269*2^4253+1)*(71596305*2^42<br \/>\n53+1)*(57309375*2^4253+1)*(56921445*2^4253+1)*(34719825*2^4253+1)*(16894545*2^4253+1)*(1792431*2^4253+1)*(97688691*2^3217+1)*(91257465*2^3217+1)*(91090419*2^3217+1)*(86093541*2^3217+1)*(85877469*2^3217+1)*(84069831*2^3217+1)*(795<br \/>\n33441*2^3217+1)*(78684369*2^3217+1)*(76317555*2^3217+1)*(76037751*2^3217+1)*(72552339*2^3217+1)*(68274339*2^3217+1)*(58155531*2^3217+1)*(53160021*2^3217+1)*(48317421*2^3217+1)*(44497059*2^3217+1)*(42114315*2^3217+1)*(41096715*2^3<br \/>\n217+1)*(39648561*2^3217+1)*(39327861*2^3217+1)*(34314159*2^3217+1)*(29652849*2^3217+1)*(24763389*2^3217+1)*(24430989*2^3217+1)*(23748699*2^3217+1)*(20007255*2^3217+1)*(18596781*2^3217+1)*(13656495*2^3217+1)*(11109435*2^3217+1)*(8<br \/>\n869755*2^3217+1)*(6894645*2^3217+1)*(5209209*2^3217+1)*(2851731*2^3217+1)*(96288201*2^2281+1)*(95937261*2^2281+1)*(95933985*2^2281+1)*(94364775*2^2281+1)*(92893239*2^2281+1)*(92748381*2^2281+1)*(90589905*2^2281+1)*(87734841*2^228<br \/>\n1+1)*(86566965*2^2281+1)*(86258499*2^2281+1)*(85734651*2^2281+1)*(84715839*2^2281+1)*(81532725*2^2281+1)*(79884849*2^2281+1)*(79081275*2^2281+1)*(76694835*2^2281+1)*(72081945*2^2281+1)*(72017001*2^2281+1)*(71253915*2^2281+1)*(688<br \/>\n93959*2^2281+1)*(68085225*2^2281+1)*(65410995*2^2281+1)*(63626145*2^2281+1)*(60039321*2^2281+1)*(56002311*2^2281+1)*(54061581*2^2281+1)*(53434575*2^2281+1)*(49409151*2^2281+1)*(41855025*2^2281+1)*(40910079*2^2281+1)*(40303905*2^2<br \/>\n281+1)*(40129041*2^2281+1)*(40018299*2^2281+1)*(31393209*2^2281+1)*(30810039*2^2281+1)*(27754761*2^2281+1)*(22185849*2^2281+1)*(20176311*2^2281+1)*(16289589*2^2281+1)*(14164635*2^2281+1)*(14147229*2^2281+1)*(11236485*2^2281+1)*(1<br \/>\n0213875*2^2281+1)*(4128945*2^2281+1)*(4039659*2^2281+1)*(4018065*2^2281+1)*(3928155*2^2281+1)*(3015531*2^2281+1)*(98028735*2^2203+1)*(97108935*2^2203+1)*(96046179*2^2203+1)*(95560221*2^2203+1)*(94884285*2^2203+1)*(94506579*2^2203<br \/>\n+1)*(91113195*2^2203+1)*(89055891*2^2203+1)*(88513845*2^2203+1)*(88293609*2^2203+1)*(87081549*2^2203+1)*(84254751*2^2203+1)*(78451869*2^2203+1)*(77693889*2^2203+1)*(76733511*2^2203+1)*(76650939*2^2203+1)*(76129479*2^2203+1)*(7458<br \/>\n5799*2^2203+1)+1<br \/>\nis prime! (3941.5612s+0.2180s)<\/p>\n<p>helper:<br \/>\n41968149*2^23209+1<br \/>\n97254741*2^21701+1<br \/>\n12450795*2^11213+1<br \/>\n20092671*2^11213+1<br \/>\n28115529*2^11213+1<br \/>\n43998375*2^11213+1<br \/>\n99539031*2^11213+1<br \/>\n14024781*2^9941+1<br \/>\n26534229*2^9941+1<br \/>\n78981231*2^9689+1<br \/>\n57506259*2^9689+1<br \/>\n24975705*2^9689+1<br \/>\n7770399*2^9689+1<br \/>\n99738639*2^4423+1<br \/>\n97478625*2^4423+1<br \/>\n96783729*2^4423+1<br \/>\n86445039*2^4423+1<br \/>\n86022459*2^4423+1<br \/>\n82860819*2^4423+1<br \/>\n82852119*2^4423+1<br \/>\n54983739*2^4423+1<br \/>\n37753119*2^4423+1<br \/>\n26448255*2^4423+1<br \/>\n26055441*2^4423+1<br \/>\n24439281*2^4423+1<br \/>\n22820631*2^4423+1<br \/>\n17436999*2^4423+1<br \/>\n14395845*2^4423+1<br \/>\n12058929*2^4423+1<br \/>\n7288671*2^4423+1<br \/>\n96317565*2^4253+1<br \/>\n82195221*2^4253+1<br \/>\n77293269*2^4253+1<br \/>\n71596305*2^4253+1<br \/>\n57309375*2^4253+1<br \/>\n56921445*2^4253+1<br \/>\n34719825*2^4253+1<br \/>\n16894545*2^4253+1<br \/>\n1792431*2^4253+1<br \/>\n97688691*2^3217+1<br \/>\n91257465*2^3217+1<br \/>\n91090419*2^3217+1<br \/>\n86093541*2^3217+1<br \/>\n85877469*2^3217+1<br \/>\n84069831*2^3217+1<br \/>\n79533441*2^3217+1<br \/>\n78684369*2^3217+1<br \/>\n76317555*2^3217+1<br \/>\n76037751*2^3217+1<br \/>\n72552339*2^3217+1<br \/>\n68274339*2^3217+1<br \/>\n58155531*2^3217+1<br \/>\n53160021*2^3217+1<br \/>\n48317421*2^3217+1<br \/>\n44497059*2^3217+1<br \/>\n42114315*2^3217+1<br \/>\n41096715*2^3217+1<br \/>\n39648561*2^3217+1<br \/>\n39327861*2^3217+1<br \/>\n34314159*2^3217+1<br \/>\n29652849*2^3217+1<br \/>\n24763389*2^3217+1<br \/>\n24430989*2^3217+1<br \/>\n23748699*2^3217+1<br \/>\n20007255*2^3217+1<br \/>\n18596781*2^3217+1<br \/>\n13656495*2^3217+1<br \/>\n11109435*2^3217+1<br \/>\n8869755*2^3217+1<br \/>\n6894645*2^3217+1<br \/>\n5209209*2^3217+1<br \/>\n96288201*2^2281+1<br \/>\n95937261*2^2281+1<br \/>\n95933985*2^2281+1<br \/>\n94364775*2^2281+1<br \/>\n92893239*2^2281+1<br \/>\n92748381*2^2281+1<br \/>\n90589905*2^2281+1<br \/>\n87734841*2^2281+1<br \/>\n86566965*2^2281+1<br \/>\n86258499*2^2281+1<br \/>\n85734651*2^2281+1<br \/>\n84715839*2^2281+1<br \/>\n81532725*2^2281+1<br \/>\n79884849*2^2281+1<br \/>\n79081275*2^2281+1<br \/>\n76694835*2^2281+1<br \/>\n72081945*2^2281+1<br \/>\n72017001*2^2281+1<br \/>\n71253915*2^2281+1<br \/>\n68893959*2^2281+1<br \/>\n68085225*2^2281+1<br \/>\n65410995*2^2281+1<br \/>\n63626145*2^2281+1<br \/>\n60039321*2^2281+1<br \/>\n56002311*2^2281+1<br \/>\n54061581*2^2281+1<br \/>\n53434575*2^2281+1<br \/>\n49409151*2^2281+1<br \/>\n41855025*2^2281+1<br \/>\n40910079*2^2281+1<br \/>\n40303905*2^2281+1<br \/>\n40129041*2^2281+1<br \/>\n40018299*2^2281+1<br \/>\n31393209*2^2281+1<br \/>\n30810039*2^2281+1<br \/>\n27754761*2^2281+1<br \/>\n22185849*2^2281+1<br \/>\n20176311*2^2281+1<br \/>\n16289589*2^2281+1<br \/>\n14164635*2^2281+1<br \/>\n14147229*2^2281+1<br \/>\n11236485*2^2281+1<br \/>\n10213875*2^2281+1<br \/>\n4128945*2^2281+1<br \/>\n4039659*2^2281+1<br \/>\n4018065*2^2281+1<br \/>\n3928155*2^2281+1<br \/>\n3015531*2^2281+1<br \/>\n98028735*2^2203+1<br \/>\n97108935*2^2203+1<br \/>\n96046179*2^2203+1<br \/>\n95560221*2^2203+1<br \/>\n94884285*2^2203+1<br \/>\n94506579*2^2203+1<br \/>\n91113195*2^2203+1<br \/>\n89055891*2^2203+1<br \/>\n88513845*2^2203+1<br \/>\n88293609*2^2203+1<br \/>\n87081549*2^2203+1<br \/>\n84254751*2^2203+1<br \/>\n78451869*2^2203+1<br \/>\n77693889*2^2203+1<br \/>\n76733511*2^2203+1<br \/>\n76650939*2^2203+1<br \/>\n76129479*2^2203+1<br \/>\n74585799*2^2203+1<\/p>\n<p>All the helpers are proven primes by pfgw N-1 method, and all of them are p+2 term of  twin prime pairs.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>18762*2*(41968149*2^23209+1)*(97254741*2^21701+1)*(12450795*2^11213+1)*(20092671*2^11213+1)*(28115529*2^11213+1)*(43998375*2^11213+1)*(99539031*2^11213+1)*(14024781*2^9941+1)*(26534229*2^9941+1)*(78981231*2^9689+1)*(57506259*2^96 89+1)*(24975705*2^9689+1)*(7770399*2^9689+1)*(99738639*2^4423+1)*(97478625*2^4423+1)*(96783729*2^4423+1)*(86445039*2^4423+1)*(86022459*2^4423+1)*(82860819*2^4423+1)*(82852119*2^4423+1)*(54983739*2^4423+1)*(37753119*2^4423+1)*(264 48255*2^4423+1)*(26055441*2^4423+1)*(24439281*2^4423+1)*(22820631*2^4423+1)*(17436999*2^4423+1)*(14395845*2^4423+1)*(12058929*2^4423+1)*(7288671*2^4423+1)*(96317565*2^4253+1)*(82195221*2^4253+1)*(77293269*2^4253+1)*(71596305*2^42 53+1)*(57309375*2^4253+1)*(56921445*2^4253+1)*(34719825*2^4253+1)*(16894545*2^4253+1)*(1792431*2^4253+1)*(97688691*2^3217+1)*(91257465*2^3217+1)*(91090419*2^3217+1)*(86093541*2^3217+1)*(85877469*2^3217+1)*(84069831*2^3217+1)*(795 33441*2^3217+1)*(78684369*2^3217+1)*(76317555*2^3217+1)*(76037751*2^3217+1)*(72552339*2^3217+1)*(68274339*2^3217+1)*(58155531*2^3217+1)*(53160021*2^3217+1)*(48317421*2^3217+1)*(44497059*2^3217+1)*(42114315*2^3217+1)*(41096715*2^3 217+1)*(39648561*2^3217+1)*(39327861*2^3217+1)*(34314159*2^3217+1)*(29652849*2^3217+1)*(24763389*2^3217+1)*(24430989*2^3217+1)*(23748699*2^3217+1)*(20007255*2^3217+1)*(18596781*2^3217+1)*(13656495*2^3217+1)*(11109435*2^3217+1)*(8 869755*2^3217+1)*(6894645*2^3217+1)*(5209209*2^3217+1)*(2851731*2^3217+1)*(96288201*2^2281+1)*(95937261*2^2281+1)*(95933985*2^2281+1)*(94364775*2^2281+1)*(92893239*2^2281+1)*(92748381*2^2281+1)*(90589905*2^2281+1)*(87734841*2^228 1+1)*(86566965*2^2281+1)*(86258499*2^2281+1)*(85734651*2^2281+1)*(84715839*2^2281+1)*(81532725*2^2281+1)*(79884849*2^2281+1)*(79081275*2^2281+1)*(76694835*2^2281+1)*(72081945*2^2281+1)*(72017001*2^2281+1)*(71253915*2^2281+1)*(688 93959*2^2281+1)*(68085225*2^2281+1)*(65410995*2^2281+1)*(63626145*2^2281+1)*(60039321*2^2281+1)*(56002311*2^2281+1)*(54061581*2^2281+1)*(53434575*2^2281+1)*(49409151*2^2281+1)*(41855025*2^2281+1)*(40910079*2^2281+1)*(40303905*2^2 281+1)*(40129041*2^2281+1)*(40018299*2^2281+1)*(31393209*2^2281+1)*(30810039*2^2281+1)*(27754761*2^2281+1)*(22185849*2^2281+1)*(20176311*2^2281+1)*(16289589*2^2281+1)*(14164635*2^2281+1)*(14147229*2^2281+1)*(11236485*2^2281+1)*(1 0213875*2^2281+1)*(4128945*2^2281+1)*(4039659*2^2281+1)*(4018065*2^2281+1)*(3928155*2^2281+1)*(3015531*2^2281+1)*(98028735*2^2203+1)*(97108935*2^2203+1)*(96046179*2^2203+1)*(95560221*2^2203+1)*(94884285*2^2203+1)*(94506579*2^2203 +1)*(91113195*2^2203+1)*(89055891*2^2203+1)*(88513845*2^2203+1)*(88293609*2^2203+1)*(87081549*2^2203+1)*(84254751*2^2203+1)*(78451869*2^2203+1)*(77693889*2^2203+1)*(76733511*2^2203+1)*(76650939*2^2203+1)*(76129479*2^2203+1)*(7458 5799*2^2203+1)+1 Proof: $ more cp1.cert $ .\/pfgw -t -h&#8221;helper&#8221; cp1 PFGW Version 3.3.2.20100216.x86_Dev [GWNUM 25.13] Resuming input file cp1 at line 2 Primality testing 18762*2*(41968149*2^23209+1)*(97254741*2^21701+1)*(12450795*2^11213+1)*(20092671*2^11213+1)*(28115529*2^11213+1)*(43998375*2^11213+1)*(99539031*2^11213+1)*(14024781*2^9941+1)*(26534229*2^9941+1)*(78981231*2^9689+1)*(57506259*2^96 89+1)*(24975705*2^9689+1)*(7770399*2^9689+1)*(99738639*2^4423+1)*(97478625*2^4423+1)*(96783729*2^4423+1)*(86445039*2^4423+1)*(86022459*2^4423+1)*(82860819*2^4423+1)*(82852119*2^4423+1)*(54983739*2^4423+1)*(37753119*2^4423+1)*(264 48255*2^4423+1)*(26055441*2^4423+1)*(24439281*2^4423+1)*(22820631*2^4423+1)*(17436999*2^4423+1)*(14395845*2^4423+1)*(12058929*2^4423+1)*(7288671*2^4423+1)*(96317565*2^4253+1)*(82195221*2^4253+1)*(77293269*2^4253+1)*(71596305*2^42 53+1)*(57309375*2^4253+1)*(56921445*2^4253+1)*(34719825*2^4253+1)*(16894545*2^4253+1)*(1792431*2^4253+1)*(97688691*2^3217+1)*(91257465*2^3217+1)*(91090419*2^3217+1)*(86093541*2^3217+1)*(85877469*2^3217+1)*(84069831*2^3217+1)*(795 33441*2^3217+1)*(78684369*2^3217+1)*(76317555*2^3217+1)*(76037751*2^3217+1)*(72552339*2^3217+1)*(68274339*2^3217+1)*(58155531*2^3217+1)*(53160021*2^3217+1)*(48317421*2^3217+1)*(44497059*2^3217+1)*(42114315*2^3217+1)*(41096715*2^3 217+1)*(39648561*2^3217+1)*(39327861*2^3217+1)*(34314159*2^3217+1)*(29652849*2^3217+1)*(24763389*2^3217+1)*(24430989*2^3217+1)*(23748699*2^3217+1)*(20007255*2^3217+1)*(18596781*2^3217+1)*(13656495*2^3217+1)*(11109435*2^3217+1)*(8 869755*2^3217+1)*(6894645*2^3217+1)*(5209209*2^3217+1)*(2851731*2^3217+1)*(96288201*2^2281+1)*(95937261*2^2281+1)*(95933985*2^2281+1)*(94364775*2^2281+1)*(92893239*2^2281+1)*(92748381*2^2281+1)*(90589905*2^2281+1)*(87734841*2^228 1+1)*(86566965*2^2281+1)*(86258499*2^2281+1)*(85734651*2^2281+1)*(84715839*2^2281+1)*(81532725*2^2281+1)*(79884849*2^2281+1)*(79081275*2^2281+1)*(76694835*2^2281+1)*(72081945*2^2281+1)*(72017001*2^2281+1)*(71253915*2^2281+1)*(688 93959*2^2281+1)*(68085225*2^2281+1)*(65410995*2^2281+1)*(63626145*2^2281+1)*(60039321*2^2281+1)*(56002311*2^2281+1)*(54061581*2^2281+1)*(53434575*2^2281+1)*(49409151*2^2281+1)*(41855025*2^2281+1)*(40910079*2^2281+1)*(40303905*2^2 281+1)*(40129041*2^2281+1)*(40018299*2^2281+1)*(31393209*2^2281+1)*(30810039*2^2281+1)*(27754761*2^2281+1)*(22185849*2^2281+1)*(20176311*2^2281+1)*(16289589*2^2281+1)*(14164635*2^2281+1)*(14147229*2^2281+1)*(11236485*2^2281+1)*(1 0213875*2^2281+1)*(4128945*2^2281+1)*(4039659*2^2281+1)*(4018065*2^2281+1)*(3928155*2^2281+1)*(3015531*2^2281+1)*(98028735*2^2203+1)*(97108935*2^2203+1)*(96046179*2^2203+1)*(95560221*2^2203+1)*(94884285*2^2203+1)*(94506579*2^2203 +1)*(91113195*2^2203+1)*(89055891*2^2203+1)*(88513845*2^2203+1)*(88293609*2^2203+1)*(87081549*2^2203+1)*(84254751*2^2203+1)*(78451869*2^2203+1)*(77693889*2^2203+1)*(76733511*2^2203+1)*(76650939*2^2203+1)*(76129479*2^2203+1)*(7458 5799*2^2203+1)+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-109","post","type-post","status-publish","format-standard","hentry","category-looking-for-a-megaprime","post-blog"],"_links":{"self":[{"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/posts\/109","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=109"}],"version-history":[{"count":0,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/posts\/109\/revisions"}],"wp:attachment":[{"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}