7000 (number) explained

Number:	7000
Roman:	MM, or
Unicode:	MM, mm,,
Lang1:	Armenian
Lang1 Symbol:	Ւ

7000 (seven thousand) is the natural number following 6999 and preceding 7001.

Selected numbers in the range 7001–7999

7001 to 7099

• 7021 – triangular number
• 7043 – Sophie Germain prime
• 7056 = 84²
• 7057 – cuban prime of the form x = y + 1,^[1] super-prime
• 7073 – Leyland number^[2]
• 7079 – Sophie Germain prime, safe prime

7100 to 7199

• 7103 – Sophie Germain prime, sexy prime with 7109
• 7106 – octahedral number^[3]
• 7109 – super-prime, sexy prime with 7103
• 7121 – Sophie Germain prime
• 7140 – triangular number, also a pronic number and hence = 3570 is also a triangular number, tetrahedral number^[4]
• 7151 – Sophie Germain prime
• 7155 – number of 19-bead necklaces (turning over is allowed) where complements are equivalent
• 7187 – safe prime
• 7192 – weird number^[5]
• 7193 – Sophie Germain prime, super-prime

7200 to 7299

• 7200 – pentagonal pyramidal number^[6]
• 7211 – Sophie Germain prime
• 7225 = 85², centered octagonal number^[7]
• 7230 = 36² + 37² + 38² + 39² + 40² = 41² + 42² + 43² + 44²
• 7246 – centered heptagonal number^[8]
• 7247 – safe prime
• 7260 – triangular number
• 7267 – decagonal number^[9]
• 7272 – Kaprekar number^[10]
• 7283 – super-prime
• 7291 – nonagonal number

7300 to 7399

• 7316 – number of 18-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 7338 – Fine number.^[11]
• 7349 – Sophie Germain prime
• 7351 – super-prime, cuban prime of the form x = y + 1
• 7381 – triangular number
• 7385 – Keith number^[12]
• 7396 = 86²

7400 to 7499

• 7417 – super-prime
• 7433 – Sophie Germain prime
• 7471 – centered cube number^[13]
• 7481 – super-prime, cousin prime

7500 to 7599

• 7503 – triangular number
• 7523 – balanced prime, safe prime, super-prime
• 7537 – prime of the form 2p-1
• 7541 – Sophie Germain prime
• 7559 – safe prime
• 7560 – highly composite number^[14]
• 7561 – Markov prime^[15]
• 7568 – centered heptagonal number
• 7569 = 87², centered octagonal number
• 7583 – balanced prime

7600 to 7699

• 7607 – safe prime, super-prime
• 7612 – decagonal number
• 7614 – nonagonal number
• 7626 – triangular number
• 7643 – Sophie Germain prime, safe prime
• 7647 – Keith number
• 7649 – Sophie Germain prime, super-prime
• 7691 – Sophie Germain prime
• 7699 – super-prime, emirp, sum of first 60 primes, first prime above 281 to be the sum of the first k primes for some k

7700 to 7799

• 7703 – safe prime
• 7710 = number of primitive polynomials of degree 17 over GF(2)
• 7714 – square pyramidal number^[16]
• 7727 – safe prime
• 7739 – member of the Padovan sequence^[17]
• 7741 = number of trees with 15 unlabeled nodes
• 7744 = 88², square palindrome not ending in 0
• 7750 – triangular number
• 7753 – super-prime
• 7770 – tetrahedral number
• 7776 = 6⁵, number of primitive polynomials of degree 18 over GF(2)
• 7777 – Kaprekar number, repdigit

7800 to 7899

• 7810 – ISO/IEC 7810 is the ISO's standard for physical characteristics of identification cards
• 7821 – n=6 value of

\sum ^{n} _{k =1} n ^{floor( (n)/() -1 k)}

• 7823 – Sophie Germain prime, safe prime, balanced prime
• 7825 – magic constant of n × n normal magic square and n-Queens Problem for n = 25. Also the first counterexample in the Boolean Pythagorean triples problem.
• 7841 – Sophie Germain prime, balanced prime, super-prime
• 7875 – triangular number
• 7883 – Sophie Germain prime, super-prime
• 7897 – centered heptagonal number

7900 to 7999

• 7901 – Sophie Germain prime
• 7909 – Keith number
• 7912 – weird number
• 7919 – 1000th prime number^[18]
• 7920 – the order of the Mathieu group M₁₁, the smallest sporadic simple group
• 7921 = 89², centered octagonal number
• 7944 – nonagonal number
• 7957 – super-Poulet number^[19]
• 7965 – decagonal number
• 7979 – highly cototient number

Prime numbers

There are 107 prime numbers between 7000 and 8000:^[20]

7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993

Notes and References

1. Web site: Sloane's A002407 : Cuban primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
2. Web site: Sloane's A076980 : Leyland numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
3. Web site: Sloane's A005900 : Octahedral numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
4. Web site: Sloane's A000292 : Tetrahedral numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
5. Web site: Sloane's A006037 : Weird numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
6. Web site: Sloane's A002411 : Pentagonal pyramidal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
7. Web site: Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
8. Web site: Sloane's A069099 : Centered heptagonal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
9. Web site: Sloane's A001107 : 10-gonal (or decagonal) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
10. Web site: Sloane's A006886 : Kaprekar numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
11. 2022-06-01.
12. Web site: Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers). The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
13. Web site: Sloane's A005898 : Centered cube numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
14. Web site: Sloane's A002182 : Highly composite numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
15. Web site: Sloane's A002559 : Markoff (or Markov) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
16. Web site: Sloane's A000330 : Square pyramidal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
17. Web site: Sloane's A000931 : Padovan sequence. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-11.
18. Web site: 7919. The Prime Pages. University of Tennessee. April 25, 2017.
19. Web site: Sloane's A050217 : Super-Poulet numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
20. Web site: Stein . William A. . William A. Stein . The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture . wstein.org . 10 February 2017 . 6 February 2021.