Primality testing Phi(3821,2963) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 23 Running N-1 test using base 41 Calling Brillhart-Lehmer-Selfridge with factored part 26.67% Phi(3821,2963) is PRP! (1904.7080s+0.0905s)

GP/PARI CALCULATOR Version 2.2.10 (alpha) i686 running linux (ix86/GMP-4.1.4 kernel) 32-bit version compiled: Sep 15 2005, gcc-3.3.2 20031022 (Red Hat Linux 3.3.2-1) (readline v4.3 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 64000000, primelimit = 500000 Testing a PRP called "Phi_3821_2963". LLL[1, 1] with [h, u]=[5, 1] has norm/bound=4.436400008 E-688 and witness=5. LLL[2, 1] with [h, u]=[5, 1] has norm/bound=0.3729775135 and witness=7. LLL[3, 1] with [h, u]=[4, 1] has norm/bound=1.057259594 E-99 and witness=3. LLL[4, 1] with [h, u]=[7, 2] has norm/bound=3.839587174 E-66 and witness=47. LLL[5, 1] with [h, u]=[7, 2] has norm/bound=0.2931494234 and witness=2. LLL[6, 1] with [h, u]=[7, 2] has norm/bound=0.2780876639 and witness=7. LLL[7, 1] with [h, u]=[7, 2] has norm/bound=0.2907265962 and witness=3. LLL[8, 1] with [h, u]=[7, 2] has norm/bound=0.3190416871 and witness=3. LLL[9, 1] with [h, u]=[7, 2] has norm/bound=0.2562215346 and witness=5. LLL[10, 1] with [h, u]=[9, 3] has norm/bound=1.535379507 E-55 and witness=29. LLL[11, 1] with [h, u]=[9, 3] has norm/bound=4.934553068 E-14 and witness=11. LLL[12, 1] with [h, u]=[9, 3] has norm/bound=0.2141565823 and witness=37. LLL[13, 1] with [h, u]=[9, 3] has norm/bound=0.2258375512 and witness=2. LLL[14, 1] with [h, u]=[9, 3] has norm/bound=0.2160944726 and witness=61. LLL[15, 1] with [h, u]=[9, 3] has norm/bound=0.1779331924 and witness=5. LLL[16, 1] with [h, u]=[9, 3] has norm/bound=0.2458638097 and witness=13. LLL[17, 1] with [h, u]=[11, 4] has norm/bound=3.951949925 E-24 and witness=2. LLL[18, 1] with [h, u]=[11, 4] has norm/bound=0.1879600406 and witness=11. LLL[19, 1] with [h, u]=[11, 4] has norm/bound=0.2106108764 and witness=13. LLL[20, 1] with [h, u]=[11, 4] has norm/bound=0.1761235534 and witness=101. LLL[21, 1] with [h, u]=[11, 4] has norm/bound=0.1929548615 and witness=83. LLL[22, 1] with [h, u]=[11, 4] has norm/bound=0.1707713333 and witness=31. LLL[23, 1] with [h, u]=[11, 4] has norm/bound=0.1928274294 and witness=71. LLL[24, 1] with [h, u]=[11, 4] has norm/bound=0.1568574031 and witness=17. LLL[25, 1] with [h, u]=[13, 5] has norm/bound=0.1266733356 and witness=61. LLL[26, 1] with [h, u]=[13, 5] has norm/bound=0.1193527275 and witness=47. LLL[27, 1] with [h, u]=[13, 5] has norm/bound=0.1420230977 and witness=79. LLL[28, 1] with [h, u]=[13, 5] has norm/bound=0.1150697941 and witness=59. LLL[29, 1] with [h, u]=[13, 5] has norm/bound=0.1266531634 and witness=101. LLL[30, 1] with [h, u]=[13, 5] has norm/bound=0.1074611888 and witness=47. LLL[31, 1] with [h, u]=[13, 5] has norm/bound=0.1172410057 and witness=3. LLL[32, 1] with [h, u]=[13, 5] has norm/bound=0.1195326339 and witness=23. LLL[33, 1] with [h, u]=[13, 5] has norm/bound=0.1334955721 and witness=7. LLL[34, 1] with [h, u]=[13, 5] has norm/bound=0.1248777288 and witness=349. LLL[35, 1] with [h, u]=[13, 5] has norm/bound=0.1276266609 and witness=3. LLL[36, 1] with [h, u]=[13, 5] has norm/bound=0.1252424612 and witness=3. LLL[37, 1] with [h, u]=[15, 6] has norm/bound=0.1006357336 and witness=2. LLL[38, 1] with [h, u]=[15, 6] has norm/bound=0.0946684291 and witness=2. LLL[39, 1] with [h, u]=[15, 6] has norm/bound=0.1040232139 and witness=107. LLL[40, 1] with [h, u]=[15, 6] has norm/bound=0.0993742563 and witness=37. LLL[41, 1] with [h, u]=[15, 6] has norm/bound=0.0970848877 and witness=2. LLL[42, 1] with [h, u]=[15, 6] has norm/bound=0.1022023459 and witness=43. LLL[43, 1] with [h, u]=[15, 6] has norm/bound=0.0920833767 and witness=47. LLL[44, 1] with [h, u]=[16, 7] has norm/bound=0.0777008415 and witness=3. LLL[45, 1] with [h, u]=[16, 7] has norm/bound=0.0807295906 and witness=31. LLL[46, 1] with [h, u]=[16, 7] has norm/bound=7.41270031 E-16 and witness=41. Validated in 33 sec. Goodbye!A copy of the self-verifying CHG certificate

`Phi_3821_2963.gp`

(7288kb) is
included in: `2963_3821.zip`

.
(2963^764-2963^573+2963^382-2963^191+1)/77051315544221 (2963^191-1)/(2962*2293*4516387*172797319*119521520205062967009183017131) 1116727839570819035825540099417 119521520205062967009183017131 111227212252446296592331 193612788851406863161 195669265541951 62820518941231 30669353495491 2542666085081 164295302531 107091547813 72621409561 331996201 172797319 69204649 6136901 4516387 2385209 1642601 877937 120331 7451 3821 2963 2293 2131 1571 1061 383 281 19 13 11 5 5 3 2 2 2

`(2963^764-2963^573+2963^382-2963^191+1)/77051315544221`

(2639 digits) and `(2963^191-1)/(2962*2293*4516387*172797319*119521520205062967009183017131)`

(613 digits) are included in: `2963_3821.zip`

Tom Wu Last modified: Mon Sep 19 21:00:36 PDT 2005