### January 30, 20042004 年 1 月 30 日 (Makoto Kamada)

# Repunit (10^49081-1)/9 and (10^86453-1)/9 are known probably prime numbers. However, following related numbers are definitely composite. No related probably prime number was found.

# 22...223<49081> = (2*10^49081+7)/9 = 2*(10^49081-1)/9+1 is divisible by 3.

# 22...223<86453> = (2*10^86453+7)/9 = 2*(10^86453-1)/9+1 is divisible by 1471.

# 22...223<98162> = (2*10^98162+7)/9 = 2*(10^(2*49081)-1)/9+1 has no factor less than 10^7 but definitely composite.

# 22...223<147243> = (2*10^147243+7)/9 = 2*(10^(3*49081)-1)/9+1 has no factor less than 10^7 but definitely composite.

# 22...223<172906> = (2*10^172906+7)/9 = 2*(10^(2*86453)-1)/9+1 is divisible by 3.

# 22...223<259359> = (2*10^259359+7)/9 = 2*(10^(3*86453)-1)/9+1 is divisible by 29.

# 66...667<49081> = (2*10^49081+1)/3 = 2*(10^49081-1)/3+1 is divisible by 7.

# 66...667<86453> = (2*10^86453+1)/3 = 2*(10^86453-1)/3+1 is divisible by 3709.

# 66...667<98162> = (2*10^98162+1)/3 = 2*(10^(2*49081)-1)/3+1 is divisible by 313.

# 66...667<147243> = (2*10^147243+1)/3 = 2*(10^(3*49081)-1)/3+1 is divisible by 43.

# 66...667<172906> = (2*10^172906+1)/3 = 2*(10^(2*86453)-1)/3+1 is divisible by 89.

# 66...667<259359> = (2*10^259359+1)/3 = 2*(10^(3*86453)-1)/3+1 has no factor less than 10^7 but definitely composite.

# 88...889<49081> = (8*10^49081+1)/9 = 8*(10^49081-1)/9+1 is divisible by 3.

# 88...889<86453> = (8*10^86453+1)/9 = 8*(10^86453-1)/9+1 is divisible by 421.

# 88...889<98162> = (8*10^98162+1)/9 = 8*(10^(2*49081)-1)/9+1 has no factor less than 10^7 but definitely composite.

# 88...889<147243> = (8*10^147243+1)/9 = 8*(10^(3*49081)-1)/9+1 is divisible by 7.

# 88...889<172906> = (8*10^172906+1)/9 = 8*(10^(2*86453)-1)/9+1 is divisible by 3.

# 88...889<259359> = (8*10^259359+1)/9 = 8*(10^(3*86453)-1)/9+1 is divisible by 7.

# 133...33<49082> = (4*10^49081-1)/3 = 4*(10^49081-1)/3+1 is divisible by 13.

# 133...33<86454> = (4*10^86453-1)/3 = 4*(10^86453-1)/3+1 is divisible by 443.

# 133...33<98163> = (4*10^98162-1)/3 = 4*(10^(2*49081)-1)/3+1 is divisible by 7.

# 133...33<147244> = (4*10^147243-1)/3 = 4*(10^(3*49081)-1)/3+1 is divisible by 31.

# 133...33<172907> = (4*10^172906-1)/3 = 4*(10^(2*86453)-1)/3+1 is divisible by 29.

# 133...33<259360> = (4*10^259359-1)/3 = 4*(10^(3*86453)-1)/3+1 is divisible by 157.

# 177...77<49082> = (16*10^49081-7)/9 = 16*(10^49081-1)/9+1 is divisible by 4297.

# 177...77<86454> = (16*10^86453-7)/9 = 16*(10^86453-1)/9+1 is divisible by 3.

# 177...77<98163> = (16*10^98162-7)/9 = 16*(10^(2*49081)-1)/9+1 is divisible by 3.

# 177...77<147244> = (16*10^147243-7)/9 = 16*(10^(3*49081)-1)/9+1 is divisible by 823.

# 177...77<172907> = (16*10^172906-7)/9 = 16*(10^(2*86453)-1)/9+1 is divisible by 19.

# 177...77<259360> = (16*10^259359-7)/9 = 16*(10^(3*86453)-1)/9+1 is divisible by 2393.

# 22...221<49082> = (2*10^49082-11)/9 = 20*(10^49081-1)/9+1 is divisible by 3.

# 22...221<86454> = (2*10^86454-11)/9 = 20*(10^86453-1)/9+1 is divisible by 379.

# 22...221<98163> = (2*10^98163-11)/9 = 20*(10^(2*49081)-1)/9+1 is divisible by 13.

# 22...221<147244> = (2*10^147244-11)/9 = 20*(10^(3*49081)-1)/9+1 is divisible by 538651.

# 22...221<172907> = (2*10^172907-11)/9 = 20*(10^(2*86453)-1)/9+1 is divisible by 3.

# 22...221<259360> = (2*10^259360-11)/9 = 20*(10^(3*86453)-1)/9+1 is divisible by 2429267.

# 33...331<49082> = (10^49082-7)/3 = 10*(10^49081-1)/3+1 is divisible by 31.

# 33...331<86454> = (10^86454-7)/3 = 10*(10^86453-1)/3+1 is divisible by 2131.

# 33...331<98163> = (10^98163-7)/3 = 10*(10^(2*49081)-1)/3+1 is divisible by 23.

# 33...331<147244> = (10^147244-7)/3 = 10*(10^(3*49081)-1)/3+1 is divisible by 29.

# 33...331<172907> = (10^172907-7)/3 = 10*(10^(2*86453)-1)/3+1 is divisible by 31.

# 33...331<259360> = (10^259360-7)/3 = 10*(10^(3*86453)-1)/3+1 is divisible by 6673.

# 355...553<49082> = (32*10^49081-23)/9 = 32*(10^49081-1)/9+1 is divisible by 3.

# 355...553<86454> = (32*10^86453-23)/9 = 32*(10^86453-1)/9+1 is divisible by 11.

# 355...553<98163> = (32*10^98162-23)/9 = 32*(10^(2*49081)-1)/9+1 is divisible by 99719.

# 355...553<147244> = (32*10^147243-23)/9 = 32*(10^(3*49081)-1)/9+1 is divisible by 11.

# 355...553<172907> = (32*10^172906-23)/9 = 32*(10^(2*86453)-1)/9+1 is divisible by 3.

# 355...553<259360> = (32*10^259359-23)/9 = 32*(10^(3*86453)-1)/9+1 is divisible by 11.

# 44...441<49082> = (4*10^49082-31)/9 = 40*(10^49081-1)/9+1 is divisible by 41.

# 44...441<86454> = (4*10^86454-31)/9 = 40*(10^86453-1)/9+1 is divisible by 3.

# 44...441<98163> = (4*10^98163-31)/9 = 40*(10^(2*49081)-1)/9+1 is divisible by 3.

# 44...441<147244> = (4*10^147244-31)/9 = 40*(10^(3*49081)-1)/9+1 is divisible by 83.

# 44...441<172907> = (4*10^172907-31)/9 = 40*(10^(2*86453)-1)/9+1 is divisible by 41.

# 44...441<259360> = (4*10^259360-31)/9 = 40*(10^(3*86453)-1)/9+1 is divisible by 1217.

# 55...551<49082> = (5*10^49082-41)/9 = 50*(10^49081-1)/9+1 is divisible by 3.

# 55...551<86454> = (5*10^86454-41)/9 = 50*(10^86453-1)/9+1 is divisible by 139.

# 55...551<98163> = (5*10^98163-41)/9 = 50*(10^(2*49081)-1)/9+1 is divisible by 2549.

# 55...551<147244> = (5*10^147244-41)/9 = 50*(10^(3*49081)-1)/9+1 is divisible by 7.

# 55...551<172907> = (5*10^172907-41)/9 = 50*(10^(2*86453)-1)/9+1 is divisible by 3.

# 55...551<259360> = (5*10^259360-41)/9 = 50*(10^(3*86453)-1)/9+1 is divisible by 7.

# 66...661<49082> = (2*10^49082-17)/3 = 20*(10^49081-1)/3+1 is divisible by 61.

# 66...661<86454> = (2*10^86454-17)/3 = 20*(10^86453-1)/3+1 is divisible by 2719.

# 66...661<98163> = (2*10^98163-17)/3 = 20*(10^(2*49081)-1)/3+1 is divisible by 19.

# 66...661<147244> = (2*10^147244-17)/3 = 20*(10^(3*49081)-1)/3+1 is divisible by 1249.

# 66...661<172907> = (2*10^172907-17)/3 = 20*(10^(2*86453)-1)/3+1 is divisible by 7.

# 66...661<259360> = (2*10^259360-17)/3 = 20*(10^(3*86453)-1)/3+1 is divisible by 29.

# 77...771<49082> = (7*10^49082-61)/9 = 70*(10^49081-1)/9+1 is divisible by 83.

# 77...771<86454> = (7*10^86454-61)/9 = 70*(10^86453-1)/9+1 is divisible by 3.

# 77...771<98163> = (7*10^98163-61)/9 = 70*(10^(2*49081)-1)/9+1 is divisible by 3.

# 77...771<147244> = (7*10^147244-61)/9 = 70*(10^(3*49081)-1)/9+1 is divisible by 19.

# 77...771<172907> = (7*10^172907-61)/9 = 70*(10^(2*86453)-1)/9+1 is divisible by 29.

# 77...771<259360> = (7*10^259360-61)/9 = 70*(10^(3*86453)-1)/9+1 has no factor less than 10^7 but definitely composite.

# 88...881<49082> = (8*10^49082-71)/9 = 80*(10^49081-1)/9+1 is divisible by 3.

# 88...881<86454> = (8*10^86454-71)/9 = 80*(10^86453-1)/9+1 is divisible by 7.

# 88...881<98163> = (8*10^98163-71)/9 = 80*(10^(2*49081)-1)/9+1 has no factor less than 10^7 but definitely composite.

# 88...881<147244> = (8*10^147244-71)/9 = 80*(10^(3*49081)-1)/9+1 is divisible by 2143.

# 88...881<172907> = (8*10^172907-71)/9 = 80*(10^(2*86453)-1)/9+1 is divisible by 3.

# 88...881<259360> = (8*10^259360-71)/9 = 80*(10^(3*86453)-1)/9+1 is divisible by 31.

# 99...991<49082> = 10^49082-9 = 10*(10^49081-1)+1 is divisible by 7.

# 99...991<86454> = 10^86454-9 = 10*(10^86453-1)+1 is divisible by 17.

# 99...991<98163> = 10^98163-9 = 10*(10^(2*49081)-1)+1 is divisible by 89.

# 99...991<147244> = 10^147244-9 = 10*(10^(3*49081)-1)+1 has no factor less than 10^7 but definitely composite.

# 99...991<172907> = 10^172907-9 = 10*(10^(2*86453)-1)+1 is divisible by 2843.

# 99...991<259360> = 10^259360-9 = 10*(10^(3*86453)-1)+1 is divisible by 2707.

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