Bruns constant and the Twin prime constant ========================================== Long double precision (80 bit). n = 1000000000000 = 1.000E+12; base (bytes) = 500000; n base eff. = 8000000 Start time: 2010-01-24 02:28:55 s CPU lm m Primes <= m Prime twins <= m Bruns constant B2 Twin prime const. ----------------------------------------------------------------------------------------------------------------------------------- 0.12 1 10 4 2 2.0637144501446804 0.8761904761904762 0.6835937500000000 0.12 2 100 25 8 1.9054552022712925 1.3309903657190868 0.6613770845471850 0.12 3 1000 168 35 1.9003539079684256 1.5180324635595910 0.6602457439708007 0.12 4 10000 1229 205 1.9036010057320106 1.6168935574322006 0.6601682965055034 0.12 5 100000 9592 1224 1.9021634758649511 1.6727995848277415 0.6601623454667365 0.13 6 1000000 78498 8169 1.9019133662823222 1.7107769308042211 0.6601618605898408 0.28 7 10000000 664579 58980 1.9021882641833462 1.7383570439172709 0.6601618197154555 1.92 8 100000000 5761455 440312 1.9021679380347306 1.7588156210679750 0.6601618161876178 18.40 9 1000000000 50847534 3424506 1.9021602393268651 1.7747359576385369 0.6601618158772920 183.87 10 10000000000 455052511 27412679 1.9021603562338200 1.7874785027192417 0.6601618158489871 1854.22 11 100000000000 4118054813 224376048 1.9021605414229175 1.7979043109551190 0.6601618158489871 18551.07 12 1000000000000 37607912018 1870585220 1.9021606304380325 1.8065924191758839 0.6601618158489871 18551.07 ln 1000000000000 37607912018 1870585220 1.9021606304380325 1.8065924191758839 0.6601618158489871 ----------------------------------------------------------------------------------------------------------------------------------- Stop time: 2010-01-24 07:38:30 Elapsed clock time: 0.21498843 days = 5.159722 hours = 18575.00 seconds /* cbrun3l32.c */ Elapsed clock time: 0.21572917 days = 5.177500 hours = 18639.00 seconds /* cbrun3l64.c */ Comment by Stefan Spaennare 2010-03-20 ====================================== The programs (cbrun3l32.c and cbrun3l64.c) were run on a 2400 MHz Intel Core 2 Duo computer with 2048 kbyte L2 cache and 4096 Mbyte DDR2 primary memory. The memory bus was 800 MHz. Operating system was Fedora 10 Linux (64-bit) and compiler Intel icc C/C++ 11.1 (64-bit) with the following options: icc -O2 -msse3 -pc80. The load was 1.00 (i.e. no other programs running). References ========== The web page "Mathematical Constants and Computation" by Xavier Gourdon and Pascal Sebah: http://numbers.computation.free.fr/Constants/constants.html