248,832 = 125, 100,00012, AKA a gross-great-gross (10012 great-grosses); the smallest fifth power that can be represented as the sum of only 6 fifth powers: 125 = 45 + 55 + 65 + 75 + 95 + 115
437,760 to 440,319 = any of these numbers will cause the
Apple II+ and
Apple IIe computers to crash to a monitor prompt when entered at the BASIC prompt, due to a short-cut in the Applesoft code programming of the overflow test when evaluating 16-bit numbers.[49] Entering 440000 at the prompt has been used to hack games that are protected against entering commands at the prompt after the game is loaded.
510,510 = the product of the first seven prime numbers, thus the seventh
primorial.[52] It is also the product of four consecutive
Fibonacci numbers—13, 21, 34, 55, the largest such sequence of any length to be also a primorial. And it is a double
triangular number, the sum of all even numbers from 0 to 1428.
777,777 = repdigit, smallest natural number requiring 20 syllables in American English, 22 in British English, largest number in English not containing the letter 'i' in its name
783,700 = initial number of third century xx00 to xx99 (after
400 and 1,400) containing seventeen
prime numbers[57][a] {783,701, 783,703, 783,707, 783,719, 783,721, 783,733, 783,737, 783,743, 783,749, 783,763, 783,767, 783,779, 783,781, 783,787, 783,791, 783,793, 783,799}
799,999 = prime number.
800,000 to 899,999
810,000 = 304
823,065 = number of trees with 20 unlabeled nodes[59]
998,001 = 9992, the largest 6-digit square. The reciprocal of this number, in its expanded form, lists all three-digit numbers in order except 998.[60]
998,991 = largest
triangular number with 6 digits and the 1413th triangular number
999,983 = largest 6-digit prime number
999,999 = repdigit.
Rational numbers with denominators 7 and 13 have 6-digit
repetends when expressed in
decimal form, because 999999 is the smallest number one less than a power of 10 that is divisible by 7 and by 13, and it is the largest number in English not containing the letter 'l' in its name.
Prime numbers
There are 9,592 primes less than 105, where 99,991 is the largest prime number smaller than 100,000.
Increments of 105 from 100,000 through a
one million have the following prime counts:
8,392 primes between 100,000 and 200,000.[b] This is a difference of
1,200 primes from the previous range.
104,729 is the 10,000th prime in this range.
199,999 is prime.
8,013 primes between 200,000 and 300,000.[c] A difference of
379 primes from the previous range.
224,737 is the 20,000th prime.
7,863 primes between 300,000 and 400,000.[d] A difference of
150 primes from the previous range.
350,377 is the 30,000th prime.
7,678 primes between 400,000 and 500,000.[e] A difference of
185 primes from the previous range. Here, the difference increases by a count of
35.
479,909 is the 40,000th prime.
7,560 primes between 500,000 and 600,000.[f] A difference of
118 primes from the previous range.
7,560 is the twentieth highly composite number.[11]
599,999 is prime.
7,445 primes between 600,000 and 700,000.[g] A difference of
115 primes from the previous range.
611,953 is the 50,000th prime.
7,408 primes between 700,000 and 800,000.[h] A difference of
37 primes from the previous range.
700,001 and 799,999 are both prime.
746,773 is the 60,000th prime.
7,323 primes between 800,000 and 900,000.[i] A difference of
85 primes from the previous range. Here, the difference increases by a count of
48.
882,377 is the 70,000th prime.
7,224 primes between 900,000 and
1,000,000.[j] A difference of
99 primes from the previous range. The difference increases again, by a count of
14.
900,001 is prime.
In total, there are 68,906 prime numbers between 100,000 and 1,000,000.[61]
Notes
^There are no centuries containing more than seventeen primes between 200 and 122,853,771,370,899 inclusive.[58]
^Smallest p > 100,000 is 100,003 (9,593rd); largest p < 200,000 is 199,999 (17,984th).
^Smallest p > 200,000 is 200,003 (17,985th); largest p < 300,000 is 299,993 (25,997th).
^Smallest p > 300,000 is 300,007 (25,998th); largest p < 400,000 is 399,989 (33,860th).
^Smallest p > 400,000 is 400,009 (33,861st); largest p < 500,000 is 499,979 (41,538th).
^Smallest p > 500,000 is 500,009 (41,539th); largest p < 600,000 is 599,999 (49,098th).
^Smallest p > 600,000 is 600,011 (49,099th); largest p < 700,000 is 699,967 (56,543rd).
^Smallest p > 700,000 is 700,001 (56,544th); largest p < 800,000 is 799,999 (63,951st).
^Smallest p > 800,000 is 800,011 (63,952nd); largest p < 900,000 is 899,981 (71,274th).
^Smallest p > 900,000 is 900,001 (71,275th); largest p <
1,000,000 is 999,983 (78,498th).
^Caldwell, Chris K."The Nth Prime Page". PrimePages. Retrieved 2022-12-03. From the differences of the
prime indexes of the smallest and largest prime numbers in ranges of increments of 105, plus 1 (for each range).
248,832 = 125, 100,00012, AKA a gross-great-gross (10012 great-grosses); the smallest fifth power that can be represented as the sum of only 6 fifth powers: 125 = 45 + 55 + 65 + 75 + 95 + 115
437,760 to 440,319 = any of these numbers will cause the
Apple II+ and
Apple IIe computers to crash to a monitor prompt when entered at the BASIC prompt, due to a short-cut in the Applesoft code programming of the overflow test when evaluating 16-bit numbers.[49] Entering 440000 at the prompt has been used to hack games that are protected against entering commands at the prompt after the game is loaded.
510,510 = the product of the first seven prime numbers, thus the seventh
primorial.[52] It is also the product of four consecutive
Fibonacci numbers—13, 21, 34, 55, the largest such sequence of any length to be also a primorial. And it is a double
triangular number, the sum of all even numbers from 0 to 1428.
777,777 = repdigit, smallest natural number requiring 20 syllables in American English, 22 in British English, largest number in English not containing the letter 'i' in its name
783,700 = initial number of third century xx00 to xx99 (after
400 and 1,400) containing seventeen
prime numbers[57][a] {783,701, 783,703, 783,707, 783,719, 783,721, 783,733, 783,737, 783,743, 783,749, 783,763, 783,767, 783,779, 783,781, 783,787, 783,791, 783,793, 783,799}
799,999 = prime number.
800,000 to 899,999
810,000 = 304
823,065 = number of trees with 20 unlabeled nodes[59]
998,001 = 9992, the largest 6-digit square. The reciprocal of this number, in its expanded form, lists all three-digit numbers in order except 998.[60]
998,991 = largest
triangular number with 6 digits and the 1413th triangular number
999,983 = largest 6-digit prime number
999,999 = repdigit.
Rational numbers with denominators 7 and 13 have 6-digit
repetends when expressed in
decimal form, because 999999 is the smallest number one less than a power of 10 that is divisible by 7 and by 13, and it is the largest number in English not containing the letter 'l' in its name.
Prime numbers
There are 9,592 primes less than 105, where 99,991 is the largest prime number smaller than 100,000.
Increments of 105 from 100,000 through a
one million have the following prime counts:
8,392 primes between 100,000 and 200,000.[b] This is a difference of
1,200 primes from the previous range.
104,729 is the 10,000th prime in this range.
199,999 is prime.
8,013 primes between 200,000 and 300,000.[c] A difference of
379 primes from the previous range.
224,737 is the 20,000th prime.
7,863 primes between 300,000 and 400,000.[d] A difference of
150 primes from the previous range.
350,377 is the 30,000th prime.
7,678 primes between 400,000 and 500,000.[e] A difference of
185 primes from the previous range. Here, the difference increases by a count of
35.
479,909 is the 40,000th prime.
7,560 primes between 500,000 and 600,000.[f] A difference of
118 primes from the previous range.
7,560 is the twentieth highly composite number.[11]
599,999 is prime.
7,445 primes between 600,000 and 700,000.[g] A difference of
115 primes from the previous range.
611,953 is the 50,000th prime.
7,408 primes between 700,000 and 800,000.[h] A difference of
37 primes from the previous range.
700,001 and 799,999 are both prime.
746,773 is the 60,000th prime.
7,323 primes between 800,000 and 900,000.[i] A difference of
85 primes from the previous range. Here, the difference increases by a count of
48.
882,377 is the 70,000th prime.
7,224 primes between 900,000 and
1,000,000.[j] A difference of
99 primes from the previous range. The difference increases again, by a count of
14.
900,001 is prime.
In total, there are 68,906 prime numbers between 100,000 and 1,000,000.[61]
Notes
^There are no centuries containing more than seventeen primes between 200 and 122,853,771,370,899 inclusive.[58]
^Smallest p > 100,000 is 100,003 (9,593rd); largest p < 200,000 is 199,999 (17,984th).
^Smallest p > 200,000 is 200,003 (17,985th); largest p < 300,000 is 299,993 (25,997th).
^Smallest p > 300,000 is 300,007 (25,998th); largest p < 400,000 is 399,989 (33,860th).
^Smallest p > 400,000 is 400,009 (33,861st); largest p < 500,000 is 499,979 (41,538th).
^Smallest p > 500,000 is 500,009 (41,539th); largest p < 600,000 is 599,999 (49,098th).
^Smallest p > 600,000 is 600,011 (49,099th); largest p < 700,000 is 699,967 (56,543rd).
^Smallest p > 700,000 is 700,001 (56,544th); largest p < 800,000 is 799,999 (63,951st).
^Smallest p > 800,000 is 800,011 (63,952nd); largest p < 900,000 is 899,981 (71,274th).
^Smallest p > 900,000 is 900,001 (71,275th); largest p <
1,000,000 is 999,983 (78,498th).
^Caldwell, Chris K."The Nth Prime Page". PrimePages. Retrieved 2022-12-03. From the differences of the
prime indexes of the smallest and largest prime numbers in ranges of increments of 105, plus 1 (for each range).