72,381,844,431,147,005,400,589,280,787,570,158,560,182,830,762,477,002,289,719,944,220,673,283,061,528,466,221,509,442,257,343,381,641,059,178,623,519,592,541,684,342,639,815,924,012,122,844,431,732,771,846,657,077,230,782,178,108,446,684,537,721,302,108,120,699,849,966,466,355,384,711,097,500,971,260,230,650,272,739,578,701,085,581,227,137,073,200,901,908,476,546,326,539,823,019,800,413,570,064,572,403,490,615,214,721,236,740,957,425,661,071,538,313,444,693,700,961,091,166,016,466,797,070,318,224,209,812,155,203,826,030,236,376,683,170,655,339,324,219,629,594,714,421,894,285,959,766,950,191,803,316,449,491,007,653,807,897,289,989,895,482,810,596,078,499,401,105,999,394,704,516,939,328,171,438,635,585,744,728,715,065,137,910,592,122,537,954,872,851,380,394,515,778,601,826,239,326,590,803,085,604,198,207,453,958,704,367,343,529,068,590,269,092,312,333,555,159,071,289,990,616,040,903,890,472,946,998,278,832,564,087,705,100,956,299,601,249,304,577

위 합성수를 소인수분해하면 m*n꼴로 나온다. (m,n 모두 메르센 소수)

m+n mod 10^9을 구하시오