List of champions for factoring Cunningham numbers: Quadratic sieve method: 3138 C116 10,142+ A. K. Lenstra & M. Manasse & al. with many computers 3195 C113 10,151- A. K. Lenstra & M. Manasse & al. with many computers Largest penultimate prime factor (ultimate factor shown also): 2894 p56*p66 7,149+ A. K. Lenstra & M. Manasse with several computers 3195 p56*p58 10,151- A. K. Lenstra & M. Manasse & al. with many computers First five holes in each table on August 3, 1991: 2,467- c133 2,479- c127 2,481- c110 2,511- c123 2,515- c114 2,481+ c122 2,485+ c116 2,487+ c147 2,491+ c123 2,503+ c151 2,802M c104 2,814L c109 2,830L c99 2,830M c100 2,838L c116 2,488+ c145 2,508+ c112 2,524+ c119 2,536+ c156 2,548+ c157 3,311- c114 3,313- c113 3,319- c119 3,331- c139 3,349- c167 3,263+ c105 3,269+ c123 3,277+ c128 3,278+ c107 3,283+ c114 5,169- c105 5,187- c106 5,229- c129 5,233- c148 5,241- c117 5,167+ c104 5,187+ c105 5,191+ c114 5,193+ c124 5,202+ c112 6,151- c105 6,163- c124 6,173- c119 6,179- c115 6,187- c107 6,164+ c125 6,169+ c101 6,172+ c99 6,176+ c125 6,178+ c137 7,163- c101 7,167- c111 7,169- c132 7,173- c146 7,187- c121 7,163+ c117 7,164+ c136 7,169+ c128 7,172+ c114 7,173+ c123 10,157- c132 10,163- c163 10,167- c142 10,169- c152 10,173- c154 10,149+ c123 10,151+ c112 10,158+ c153 10,163+ c139 10,166+ c164 11,131- c134 11,145- c113 11,151- c139 11,159- c96 11,167- c128 11,127+ c120 11,131+ c129 11,139+ c114 11,140+ c98 11,142+ c141 12,137- c123 12,139- c119 12,149- c156 12,151- c162 12,161- c135 12,127+ c99 12,131+ c136 12,136+ c104 12,139+ c100 12,146+ c140 Ten Most Wanted Factorizations (from Update 2.4) 1. 2,1024+ C291 6. 10,151- C139* 2. 5,256+ C134 7. 10,149+ C123 3. 2,428+ C114* 8. 12,118+ C110* 4. 2,467- C133 9. 11,127+ C120 5. 2,479- C127 10. 3,257- C118* Twenty-Four More Wanted Factorizations 2,445- C103* 2,463+ C101* 2,499+ C104* 3,263+ C105 2,481- C110 2,479+ C108* 2,722M C103* 5,169- C105 2,427+ C98* 2,481+ C122 2,460+ C106* 5,167+ C104 2,439+ C105* 2,485+ C116 2,488+ C145 6,151- C105 2,443+ C105* 2,487+ C147 2,496+ C114* 6,163- C124 2,461+ C102* 2,491+ C123 3,227- C98* 6,164+ C125 * = was factored on Page 62 or Page 63