Residue Distribution
Analyze how primes distribute across modular classes (mod 6, mod 10, etc). Understand prime congruence patterns.
Tools / Mathematical Discovery
prime_residue
$0.15 per call
Analyze prime number residue patterns and distributions. Discover patterns in prime congruences, modular arithmetic, and prime gaps. Essential for number theory research.
Capabilities
Twin Prime Detection
Count prime pairs (p, p+2) and analyze their distribution across ranges.
Gap Analysis
Calculate average and maximum gaps between consecutive primes in your range.
Density Statistics
Compute prime density across different ranges for research applications.
API Demo
prime_residue
// Request
{"name": "prime_residue", "arguments": {"n_primes": 1000}}
// Response
{
"primes_analyzed": 1000,
"largest_prime": 7919,
"residue_mod_6": {"1": 499, "5": 500},
"twin_prime_count": 35,
"average_gap": 6.4,
"max_gap": 36
}
Cost: $0.15 (15 credits)
Use Cases
Number Theory Research
Explore prime distributions and test conjectures computationally.
Cryptography Analysis
Understand prime density for key generation parameters.
Educational Tools
Visualize prime patterns for teaching number theory.
Start discovering prime patterns today
Access advanced mathematical discovery tools. $0.15 per call, no commitment required.
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