{"uid":"cap_ZXgcB_EMV_o5kNsRersL6","slug":"numora-mersenne-number-generator-69b87a05","name":"Numora Mersenne Number Generator","description":"100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.","url":"https://numomo.vercel.app/api/number/mersenne","method":"POST","headers":{},"bodySchema":{"type":"object","required":["exponent"],"properties":{"exponent":{"type":"integer"}}},"responseSchema":{"type":"object","required":["success","result","computation"],"properties":{"result":{"type":"object","description":"Computation result varies by endpoint"},"success":{"type":"boolean","description":"Always true on success"},"computation":{"type":"string","description":"Human-readable description of what was computed"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_B5MS_PCmtPGA85SLxjgRu","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes whether a given integer exponent produces a Mersenne prime (2^p - 1) and returns the resulting Mersenne number and its properties","exampleAgentPrompt":"Can you compute the Mersenne number for exponent 31 and tell me whether it's a Mersenne prime?","exampleUseCases":[{"title":"Verify Mersenne prime for research","prompt":"I'm studying number theory — can you check if exponent 61 produces a Mersenne prime and give me the full value of 2^61 - 1?"},{"title":"Educational prime number exploration","prompt":"I'm teaching a math class about prime numbers — can you compute the Mersenne number for exponent 7 and explain whether it's prime?"},{"title":"Cryptography study: large prime lookup","prompt":"For a cryptography exercise, I need to know if exponent 127 yields a Mersenne prime — can you calculate 2^127 - 1 and tell me if it's prime?"}],"resultDescription":"Returns a JSON object with success (boolean), result (object containing the Mersenne number 2^p-1, whether it is prime, the exponent used, and related numeric properties), and computation (a human-readable string describing what was calculated).","failureModes":["Missing or non-integer exponent returns a validation error","Exponent too large may cause timeout or overflow","Negative or zero exponent may return an error or unexpected result","Payment failure via x402 returns 402 status before computation begins"],"whenToPreferThis":"Choose this endpoint when you need to compute or verify Mersenne numbers (2^p - 1) and their primality for a specific integer exponent, especially in number theory research, educational math contexts, or cryptography applications. Prefer this over general-purpose math libraries when you need a simple pay-per-call API with no setup, and over symbolic math APIs when you want a fast numeric result with a human-readable explanation included.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T18:57:35.547Z","isFirstParty":false}