1001 - sphenic number (7 x 11 x 13), pentagonal number, pentatope number
1002 - sphenic number, Mertens function zero, abundant number
1003 - semiprime (17 × 59)
1005 - Mertens function zero
1008 - divisible by the number of primes below it
1009 - first prime above 1000
1010 - Mertens function zero
1013 - Sophie Germain prime, centered square number, Mertens function zero
1014 - Mertens function zero
1015 - square pyramidal number
1018 - Mertens function zero
1019 - Sophie Germain prime, safe prime
1020 - polydivisible number
1023 - is the highest number one can count to on one's fingers using binary
1024 - power of two, 32^2; in common use, the amount of bytes in a kilobyte (in 1999, the IEC coined kibibyte to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted)
1027 - sum of the squares of the first eight primes
1028 - sum of totient function for first 58 integers
1031 - Sophie Germain prime
1035 - triangular number, hexagonal number
1049 - Sophie Germain prime, highly cototient number
1051 - centered pentagonal number
1056 - pronic number
1060 - sum of the first 25 primes
1071 - heptagonal number
1072 - centered heptagonal number
1079 - every positive integer is the sum of at most 1079 tenth powers.
1080 - pentagonal number
1081 - triangular number, member of Padovan sequence
1086 - Smith number, sum of totient function for first 59 integers
1087 - Chen prime, cousin prime, lucky prime, Kynea number
1089 - 33^2, nonagonal number, centered octagonal number
1091 - cousin prime and twin prime
1092- divisible by the number of primes below it
1093 - twin prime and star number
1102 - sum of totient function for first 60 integers
1103 - Sophie Germain prime, balanced prime
1104 - Keith number
1105 - Carmichael number, magic constant of n × n magic square and n-Queens Problem for n = 13, decagonal number, centered square number
1116 - divisible by the number of primes below it
1122 - pronic number, divisible by the number of primes below it
1123 - balanced prime
1124 - Leyland number
1128 - triangular number, hexagonal number, divisible by the number of primes below it
1134- divisible by the number of primes below it
1138 - special code for Easter eggs on Star Wars DVDs, because of George Lucas's movie THX 1138
1140 - tetrahedral number
1152 - highly totient number
1156 - 34^2, octahedral number, centered pentagonal number
1161 - sum of the first 26 primes
1162 - pentagonal number, sum of totient function for first 61 integers
1169 - highly cototient number
1170 - highest possible score in an NAQT match
1176 - triangular number
1177 - heptagonal number
1184 - amicable number with 1210
1187 - safe prime, Stern prime, balanced prime
1190 - pronic number
1192 - sum of totient function for first 62 integers
1198 - centered heptagonal number
1200 - the number of households the Nielsen ratings sample
1201 - centered square number
1210 - amicable number with 1184
1216 - nonagonal number
1219 - Mertens function zero
1220 - Mertens function zero
1223 - Sophie Germain prime, balanced prime
1225 - triangular number, 35^2, triangular square number, hexagonal number, centered octagonal number
1228 - sum of totient function for first 63 integers
1229 - Sophie Germain prime
1233 - 12^2 + 33^2
1240 - square pyramidal number
1241 - centered cube number
1242 - decagonal number
1247 - pentagonal number