{
"messages": [
{
"role": "user",
"content": "Are there an infinite number of prime numbers such that n mod 4 == 3?"
},
{
"role": "assistant",
"content": "Yes, there are infinitely many prime numbers such that n ≡ 3 (mod 4).\n\nThis is a classic theorem in number theory, and here's a proof…",
"reasoning_content": "This is asking about whether there are infinitely many prime numbers that are congruent to 3 modulo 4, i.e., primes of the form 4k + 3.\n\nLet me think about this systematically. First…",
"thinking_blocks": [
{
"type": "thinking",
"thinking": "This is asking about whether there are infinitely many prime numbers that are congruent to 3 modulo 4, i.e…",
"signature": "EswgCkYIBhgCKkDCG…"
}
],
"tool_calls": []
}
]
}