← The evidence ledger
Evidence row 120406
Observed , by baseline/1.
- Kind
- listing
- About
- source_record x402_bazaar:https://saylorinnovations.com/api/math/number-theory
- Recorded
- Previous row
- None: the first of its kind about this subject
- Body SHA-256
- 644e107d7a173bfed010c8dddc409a7df6aae0f4e3a9912008edda161966b25c
- Leaf
- 0x075d5d5434b25f204db5a15a15e3ea14c9e5f38f3f089d9060e4d4bff19773e2
What was observed
{
"endpoints": [
[
"x402",
"https://saylorinnovations.com/api/math/number-theory"
]
],
"name": "Saylor Innovations Data Desk",
"owner_address": "0xa2a8df0f7caabea4e120a2568118f141569fc8aa",
"raw": {
"accepts": [
{
"amount": "10000",
"asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
"extra": {
"assetTransferMethod": "eip3009",
"facilitatorOnly": true,
"memo": "saylor:datadesk:number-theory",
"name": "USD Coin",
"note": "Base settles through an x402 facilitator. Send payload.signature and payload.authorization (EIP-3009); there is no self-submitted path on this network.",
"version": "2"
},
"maxTimeoutSeconds": 120,
"network": "eip155:8453",
"payTo": "0xA2A8dF0f7CaaBEa4e120a2568118f141569fc8aa",
"scheme": "exact"
},
{
"amount": "10000",
"asset": "0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359",
"extra": {
"assetTransferMethod": "eip3009",
"facilitatorOnly": true,
"memo": "saylor:datadesk:number-theory",
"name": "USD Coin",
"note": "Polygon settles through an x402 facilitator. Send payload.signature and payload.authorization (EIP-3009); there is no self-submitted path on this network.",
"version": "2"
},
"maxTimeoutSeconds": 120,
"network": "eip155:137",
"payTo": "0xA2A8dF0f7CaaBEa4e120a2568118f141569fc8aa",
"scheme": "exact"
},
{
"amount": "10000",
"asset": "0xaf88d065e77c8cC2239327C5EDb3A432268e5831",
"extra": {
"assetTransferMethod": "eip3009",
"facilitatorOnly": true,
"memo": "saylor:datadesk:number-theory",
"name": "USD Coin",
"note": "Arbitrum settles through an x402 facilitator. Send payload.signature and payload.authorization (EIP-3009); there is no self-submitted path on this network.",
"version": "2"
},
"maxTimeoutSeconds": 120,
"network": "eip155:42161",
"payTo": "0xA2A8dF0f7CaaBEa4e120a2568118f141569fc8aa",
"scheme": "exact"
},
{
"amount": "10000",
"asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v",
"extra": {
"feePayer": "D6ZhtNQ5nT9ZnTHUbqXZsTx5MH2rPFiBBggX4hY1WePM",
"memo": "saylor:datadesk:number-theory",
"reference": "DXAeuPMtpF1YvGdA12ZUiHr5TMjmPXxJrioeHYuxVt4S",
"session": "eyJhcnRpY2xlSWQiOiJkYXRhZGVzazpudW1iZXItdGhlb3J5IiwicmVmZXJlbmNlIjoiRFhBZXVQTXRwRjFZdkdkQTEyWlVpSHI1VE1qbVBYeEpyaW9lSFl1eFZ0NFMiLCJyZWNpcGllbnQiOiI3TFNqZnJKZjhmTnNCOFZBOXU3TjNXRW4yNXNtUUxwb2IzU3Z5VXZYYWN5NyIsIm1pbnQiOiJFUGpGV2RkNUF1ZnFTU3FlTTJxTjF4enliYXBDOEc0d0VHR2tad3lURHQxdiIsIm1pbkFtb3VudCI6MTAwMDAsImV4cCI6MTc5MjM3NzQ3MDgxMX0.4bJ7jk7p-wpToZBjReV42RBUe1qIuaRFQt9kO_ZVWUc"
},
"maxTimeoutSeconds": 120,
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"payTo": "7LSjfrJf8fNsB8VA9u7N3WEn25smQLpob3SvyUvXacy7",
"scheme": "exact"
},
{
"amount": "10000",
"asset": "Es9vMFrzaCERmJfrF4H2FYD4KCoNkY11McCe8BenwNYB",
"extra": {
"feePayer": "D6ZhtNQ5nT9ZnTHUbqXZsTx5MH2rPFiBBggX4hY1WePM",
"memo": "saylor:datadesk:number-theory",
"reference": "EW8j9T3F4zSyfoBdpm465CrKtizQEA2PkGGdpEkqCxtD",
"session": "eyJhcnRpY2xlSWQiOiJkYXRhZGVzazpudW1iZXItdGhlb3J5IiwicmVmZXJlbmNlIjoiRVc4ajlUM0Y0elN5Zm9CZHBtNDY1Q3JLdGl6UUVBMlBrR0dkcEVrcUN4dEQiLCJyZWNpcGllbnQiOiI3TFNqZnJKZjhmTnNCOFZBOXU3TjNXRW4yNXNtUUxwb2IzU3Z5VXZYYWN5NyIsIm1pbnQiOiJFczl2TUZyemFDRVJtSmZyRjRIMkZZRDRLQ29Oa1kxMU1jQ2U4QmVud05ZQiIsIm1pbkFtb3VudCI6MTAwMDAsImV4cCI6MTc5MjM3NzQ3MDgxMX0.CQG5FU8p3Q-fo9akLi0nGO3-tCY5SBK2CYAm-PJnzgY"
},
"maxTimeoutSeconds": 120,
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"payTo": "7LSjfrJf8fNsB8VA9u7N3WEn25smQLpob3SvyUvXacy7",
"scheme": "exact"
},
{
"amount": "92504",
"asset": "So11111111111111111111111111111111111111112",
"extra": {
"memo": "saylor:datadesk:number-theory",
"native": true,
"note": "Native SOL: send lamports with a system transfer, not an SPL transfer. Price is quoted live and this quote expires in 120s.",
"quotedLamports": "95365",
"reference": "Cf8y7DNf98NR9aknMqGNA2W4exhTxtSkTziiT6fiUKse",
"session": "eyJhcnRpY2xlSWQiOiJkYXRhZGVzazpudW1iZXItdGhlb3J5IiwicmVmZXJlbmNlIjoiQ2Y4eTdETmY5OE5SOWFrbk1xR05BMlc0ZXhoVHh0U2tUemlpVDZmaVVLc2UiLCJyZWNpcGllbnQiOiI3TFNqZnJKZjhmTnNCOFZBOXU3TjNXRW4yNXNtUUxwb2IzU3Z5VXZYYWN5NyIsIm1pbnQiOm51bGwsIm1pbkFtb3VudCI6OTI1MDQsImV4cCI6MTc5MjM3NzQ3MDgxMX0.dkLCPcGh8kdCSs76pnzQimDgh0hGQlZfyX4FdcWbtXk",
"solUsdPrice": 104.86
},
"maxTimeoutSeconds": 120,
"network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
"payTo": "7LSjfrJf8fNsB8VA9u7N3WEn25smQLpob3SvyUvXacy7",
"scheme": "exact"
}
],
"description": "Number toolkit - primality, prime factorization, divisors, totient, perfect or abundant class, roman numeral, English words, bases and gcd or lcm with a second number",
"extensions": {
"bazaar": {
"info": {
"input": {
"method": "GET",
"queryParams": {
"m": "84",
"n": "360360"
},
"type": "http"
},
"output": {
"example": {
"aliquot_sum": 1212120,
"binary": "1010111111110101000",
"classification": "abundant",
"digit_count": 6,
"digit_sum": 18,
"digital_root": 9,
"distinct_prime_factors": 6,
"divisor_count": 192,
"divisor_sum": 1572480,
"euler_totient": 69120,
"hexadecimal": "57FA8",
"in_words": "three hundred sixty thousand three hundred sixty",
"is_even": true,
"is_palindrome": false,
"is_perfect_cube": false,
"is_perfect_square": false,
"is_power_of_two": false,
"is_prime": false,
"n": 360360,
"next_prime": 360391,
"note": "Primality uses deterministic Miller-Rabin (exact for numbers below 2^53); factorization is trial division up to 10^14. Pass m to also get gcd and lcm.",
"octal": "1277650",
"previous_prime": 360337,
"prime_factorization": "2^3 x 3^2 x 5 x 7 x 11 x 13",
"prime_factors": [
2,
3,
5,
7,
11,
13
],
"roman_numeral": null,
"source": "number theory",
"with_m": {
"coprime": false,
"gcd": 84,
"lcm": 360360,
"m": 84
}
},
"type": "json"
}
},
"schema": {
"$schema": "https://json-schema.org/draft/2020-12/schema",
"properties": {
"input": {
"additionalProperties": false,
"properties": {
"method": {
"enum": [
"GET"
],
"type": "string"
},
"queryParams": {
"properties": {
"m": {
"description": "optional second number for gcd and lcm",
"type": "string"
},
"n": {
"description": "Whole number 0 to 9007199254740991",
"type": "string"
}
},
"required": [
"n"
],
"type": "object"
},
"type": {
"const": "http",
"type": "string"
}
},
"required": [
"type",
"method"
],
"type": "object"
},
"output": {
"properties": {
"example": {
"properties": {
"aliquot_sum": {
"description": "Aliquot sum",
"type": [
"number",
"null"
]
},
"binary": {
"description": "Binary representation",
"type": "string"
},
"classification": {
"description": "Classification assigned by the source",
"type": [
"string",
"null"
]
},
"digit_count": {
"description": "Number of digit",
"type": [
"number",
"null"
]
},
"digit_sum": {
"description": "Digit sum",
"type": "number"
},
"digital_root": {
"description": "Digital root",
"type": [
"number",
"null"
]
},
"distinct_prime_factors": {
"description": "Distinct prime factors",
"type": [
"number",
"null"
]
},
"divisor_count": {
"description": "Number of divisor",
"type": [
"number",
"null"
]
},
"divisor_sum": {
"description": "Divisor sum",
"type": [
"number",
"null"
]
},
"euler_totient": {
"description": "Euler totient",
"type": [
"number",
"null"
]
},
"hexadecimal": {
"description": "Hexadecimal representation",
"type": "string"
},
"in_words": {
"description": "In words",
"type": "string"
},
"is_even": {
"description": "True when this is even",
"type": [
"boolean",
"null"
]
},
"is_palindrome": {
"description": "True when this is palindrome",
"type": [
"boolean",
"null"
]
},
"is_perfect_cube": {
"description": "True when this is perfect cube",
"type": [
"boolean",
"null"
]
},
"is_perfect_square": {
"description": "True when this is perfect square",
"type": "boolean"
},
"is_power_of_two": {
"description": "True when this is power of two",
"type": [
"boolean",
"null"
]
},
"is_prime": {
"description": "True when this is prime",
"type": "boolean"
},
"n": {
"description": "The integer analysed",
"type": "number"
},
"next_prime": {
"description": "Next prime",
"type": [
"number",
"null"
]
},
"note": {
"description": "Caveat or context for reading the result",
"type": "string"
},
"octal": {
"description": "Octal representation",
"type": [
"string",
"null"
]
},
"previous_prime": {
"description": "Previous prime",
"type": [
"number",
"null"
]
},
"prime_factorization": {
"description": "Prime factorization",
"type": [
"string",
"null"
]
},
"prime_factors": {
"description": "Prime factors",
"type": [
"array",
"null"
]
},
"roman_numeral": {
"description": "Roman numeral",
"type": [
"string",
"null"
]
},
"source": {
"description": "Data source the values come from",
"type": "string"
},
"with_m": {
"description": "With m",
"properties": {
"coprime": {
"description": "True when n and m share no factor",
"type": [
"boolean",
"null"
]
},
"gcd": {
"description": "Greatest common divisor with m",
"type": [
"number",
"null"
]
},
"lcm": {
"description": "Least common multiple with m",
"type": [
"number",
"null"
]
},
"m": {
"description": "Second number supplied",
"type": [
"number",
"null"
]
}
},
"type": "object"
}
},
"required": [
"n",
"is_prime",
"in_words"
],
"type": "object"
},
"type": {
"const": "json",
"type": "string"
}
},
"required": [
"type"
],
"type": "object"
}
},
"required": [
"input"
],
"type": "object"
}
}
},
"iconUrl": "https://res.cloudinary.com/bdb-prod/image/upload/c_fill,ar_1:1,w_256,h_256,f_auto,q_auto/v1791811517/bazaar-icons/bc5e2b3d111ebbef.jpg",
"lastUpdated": "2026-10-19T02:35:50.847Z",
"quality": {
"l30DaysTotalCalls": 2,
"l30DaysUniquePayers": 2,
"lastCalledAt": "2026-10-19T02:35:50.657Z"
},
"resource": "https://saylorinnovations.com/api/math/number-theory",
"serviceName": "Saylor Innovations Data Desk",
"tags": [
"is this number prime",
"prime factorization of a number",
"number to roman numeral",
"number to english words",
"gcd and lcm of two numbers"
],
"type": "http",
"x402Version": 2
},
"source": "x402_bazaar",
"summary": "Number toolkit - primality, prime factorization, divisors, totient, perfect or abundant class, roman numeral, English words, bases and gcd or lcm with a second number"
}What the leaf hashes
{"body":"644e107d7a173bfed010c8dddc409a7df6aae0f4e3a9912008edda161966b25c","id":120406,"kind":"listing","method":"baseline/1","observed_us":1793025618014349,"prev":null,"subject":"x402_bazaar:https://saylorinnovations.com/api/math/number-theory","subject_kind":"source_record"}Proof
Fold these into the leaf in order, hashing each sorted pair with keccak256, to reach the root of (296695 rows).
- 0x075d734bf59fc745b1a69c004a09113bd8a0187dc92c1be2e1569df6360d9917
- 0xef0f6cf1d11625222b4e4513c9dd0d5ad2b022fa18c7b3485c59e01aec1aa946
- 0x4bf035b0dbb7abdef48d29f774331c70cf30137893933f8c6171899b1ab40ffb
- 0x172ad8b6cc85d6bb19d07b25b1f223ce218d3094e83feed34284fd0982989a87
- 0x3a9475fad8ef4c18e4210c6a323b23fb7135ba93a2a73b1b7b1ede0c0cf783f4
- 0x3e2cecc83cb4b32edc5f327e311245b6ece78a627fdc4923d4474d412f34d381
- 0x6f5e76475e208d2cc4827cc6f17da5aae2ec93a88d54247c2277cac2b0390bbb
- 0x4349ee58dba33697618d38e81dd2949c556742e1accc531a9420d0bce14d8369
- 0x5f760c3d7b808d6842869f52ca2b76210089da142e118d10f4b9883456957c20
- 0x6c49dc63732a1c853796427378de391ae7c0255d6d855269049c50243c7bc2b5
- 0xe5919b091405f2537da4d32a97f1520286a61795e2d149438b884ef5190051cc
- 0x6003e14d04cde1d24b195ac15b568dd483e04047e0f2ff64d9632a51a8f7123d
- 0xe5a836cf25a8dfc72c9e3b6a69a7561a1f61f50f9cf36707d36f6e926aa15dec
- 0xa96bb9408ce00a0d40ddaba8736257dfce76d5478b131d69db1afdf8a824312b
- 0x7ddc2fead128357f881b63e6c7c26d7fbbb84fca6c7c8e0bbfe386de86ca8d39
- 0xc6a4d7899a0f442958e26505011190b7cff2483611c1b94eba9043e0ba9ac36e
- 0x8c756542e482157df0c36464d75c937b845e4423dbbcfad08f0cf8d5a16b9a13
- 0x20704208aa6923d6b2450ef74ede87a6e0265d46447926038fe9506e9e154b2d
- 0x9b9ce5b74b9bab5121612ef6b64920a8d453cbf311096a423eef9702747e868a
- Day root
- 0xf43e8dcc3d451a4788b26be904c55e8c4c0fa75c9666796c51db38d37e2c0df8
- Chained
- 0x702d5ac508f08b0d1accf36af25822d8e5660367494edd17a642fb61e158a57a
- Published
- On Arc Testnet, block 69251483: 0x495162f8936e19f0039918feebe6c307f327cd6bf8c37219620b1970041fa9ae