Sierpiński number

Target entity: Sierpiński number
Context triple: [Wacław Sierpiński, notableIdea, Sierpiński number]

• A. Fermat number
  A Fermat number is a special type of integer of the form \(F_n = 2^{2^n} + 1\), studied in number theory for its intriguing properties related to primality and constructible polygons.
• B. Carmichael number
  A Carmichael number is a composite integer that nonetheless satisfies Fermat's primality test for all bases coprime to it, making it a classic example of a Fermat pseudoprime.
• C. Blum integer
  A Blum integer is a special type of composite number formed as the product of two distinct prime numbers each congruent to 3 modulo 4, widely used in cryptography and pseudorandom number generation.
• D. Sylvester sequence
  The Sylvester sequence is an integer sequence defined recursively where each term is one more than the product of all previous terms, yielding rapidly growing, pairwise coprime numbers closely related to Egyptian fraction representations.
• E. Bateman–Horn conjecture
  The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Sierpiński number
Target entity description: A Sierpiński number is an odd positive integer k such that k·2ⁿ + 1 is composite for all natural numbers n, making it central to a famous unsolved problem in number theory.

• A. Fermat number
  A Fermat number is a special type of integer of the form \(F_n = 2^{2^n} + 1\), studied in number theory for its intriguing properties related to primality and constructible polygons.
• B. Carmichael number
  A Carmichael number is a composite integer that nonetheless satisfies Fermat's primality test for all bases coprime to it, making it a classic example of a Fermat pseudoprime.
• C. Blum integer
  A Blum integer is a special type of composite number formed as the product of two distinct prime numbers each congruent to 3 modulo 4, widely used in cryptography and pseudorandom number generation.
• D. Sylvester sequence
  The Sylvester sequence is an integer sequence defined recursively where each term is one more than the product of all previous terms, yielding rapidly growing, pairwise coprime numbers closely related to Egyptian fraction representations.
• E. Bateman–Horn conjecture
  The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
• F. None of above. chosen