A prime number p is called special if there exist primes p1, p2, p3, p

1.	A prime number p is called special if there exist primes p1, p2, p3, p4 such that p = p1 + p2 = p3 - p4. The number of special primes is(a) 0(b) 1(c) more than one but finite(d) infinite
Answer» Answer is : (b) 1 It is given that for prime numbers p₁, p₂, p₃, p₄ the special prime number p = p₁ + p₂ = p₃ - p₄ Case I If all p₁, p₂, p₃, p₄ are odd, then (p₁ + p₂ ) and (p₃ - p₄) are even, which is not possible. Case II If one of p₁ and p₂ is even, say p₂ is 2 and p₄ must be 2. So, p = p₁ + 2 = p₃ - 2 the above equation is satisfied only if p = 5, p₁ = 3 and p₃ = 7 So, the number of special prime p is 1.

A prime number p is called special if there exist primes p1, p2, p3, p4 such that p = p1 + p2 = p3 - p4. The number of special primes is(a) 0(b) 1(c) more than one but finite(d) infinite

Answer»

Answer is : (b) 1

It is given that for prime numbers p₁, p₂, p₃, p₄ the special prime number

p = p₁ + p₂ = p₃ - p₄

Case I

If all p₁, p₂, p₃, p₄ are odd, then (p₁ + p₂ ) and (p₃ - p₄) are even, which is not possible.

Case II

If one of p₁ and p₂ is even, say p₂ is 2 and p₄ must be 2.

So, p = p₁ + 2 = p₃ - 2

the above equation is satisfied only if

p = 5, p₁ = 3 and p₃ = 7

So, the number of special prime p is 1.

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A prime number p is called special if there exist primes p1, p2, p3, p4 such that p = p1 + p2 = p3 - p4. The number of special primes is(a) 0(b) 1(c) more than one but finite(d) infinite

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