Chebyshev bias

Target entity: Chebyshev bias
Context triple: [Pafnuty Chebyshev, notableWork, Chebyshev bias]

• A. Chebyshev’s estimates for π(x)
  Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number theorem.
• B. Montgomery's pair correlation conjecture
  Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
• C. Turán–Kubilius inequality
  The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
• D. Siegel–Walfisz theorem
  The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
• E. Linnik’s theorem on the least prime in an arithmetic progression
  Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Chebyshev bias
Target entity description: Chebyshev bias is a phenomenon in number theory describing the tendency for primes to favor certain residue classes modulo a given integer, particularly the apparent predominance of primes congruent to 3 rather than 1 modulo 4.

• A. Chebyshev’s estimates for π(x)
  Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number theorem.
• B. Montgomery's pair correlation conjecture
  Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
• C. Turán–Kubilius inequality
  The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
• D. Siegel–Walfisz theorem
  The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
• E. Linnik’s theorem on the least prime in an arithmetic progression
  Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
• F. None of above. chosen