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90 Chapter 2. On a conjecture about addition modulo 2 k − 1Tu and Deng were able to check the original conjecture (Conjecture 1.2.2) for k ≤ 29 in aboutfifteen days on a PC with a Pentium4 CPU cadenced at 3.2 GHz and 256 Mb of RAM [264,Appendix]. Using our implementation, we were able to check the conjecture for k = 39 in abouttwelve hours and fifteen minutes on a pool of about four hundred quite recent cores and for k = 40on a subset of them. More details on the computers used are given in Tables 2.5 and 2.6. Sometimings are given in Table 2.7. The complete source code of our implementation is available atthe following address: http://www.infres.enst.fr/~flori/.Table 2.5: Computers’ description — Part IID CPU Clock rate Cores NumberA Dual-Core AMD Opteron(tm) Processor 1222 3 GHz 2 20B Intel(R) Core(TM)2 Quad CPU Q9400 2.66 GHz 4 20C Intel(R) Xeon(R) CPU W3520 2.67 GHz 8 17D Intel(R) Core(TM)2 Duo CPU E8600 3.33 GHz 2 23E Intel(R) Core(TM)2 Duo CPU E8500 3.16 GHz 2 33F Intel(R) Xeon(R) CPU E5540 2.53 GHz 16 1G Intel(R) Xeon(R) CPU X5690 3.47 GHz 24 1H Intel(R) Core(TM)2 Quad CPU Q6600 2.40 GHz 4 1Table 2.6: Computers’ description — Part IIID Distribution Linux versionA Debian 6.0.2 2.6.32-5-amd64B Debian 6.0.2 2.6.32-5-amd64C Debian 6.0.2 2.6.32-5-amd64D Debian 6.0.2 2.6.32-5-amd64E Fedora release 15 (Lovelock) 2.6.40.4-5.fc15.x86_64F Scientific Linux CERN SLC2.6.32-71.29.1.el6.x86_64release 6.1 beta (Carbon)G CentOS Linux release 6.0 (Final) 2.6.32-71.29.1.el6.centos.plus.x86_64H Debian wheezy/sid 3.0.0-1-amd64