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Block #59,482

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 2:28:53 AM Β· Difficulty 8.9651 Β· 6,767,248 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
cce3f559b720d639b9ca50ad97f26ff967fe4bd498314ed7cbbeea8c88f6dc72
View on Chainz β†—

Height

#59,482

Difficulty

8.965105

Transactions

2

Size

692 B

Version

2

Bits

08f71119

Nonce

285

Timestamp

7/18/2013, 2:28:53 AM

Confirmations

6,767,248

Merkle Root

7b0fe3d316670b6712ef98408c2e3e07f3e77e11c448f165b93be0a96de02ba9
Transactions (2)
Coinbase941665452eac9a…fe735ed02259e7
1 in β†’ 1 out12.4300 XPM110 B
APBGTBJf…Y9gCcZLa
f4c384b6f9cf92…1ac1b6e2d512f4
3 in β†’ 1 out299.9000 XPM488 B
AMKxJqj9…CM2SJHqp
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.477 Γ— 10¹⁰³(104-digit number)
14770737627893255584…91209932192567397920
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.477 Γ— 10¹⁰³(104-digit number)
14770737627893255584…91209932192567397921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.954 Γ— 10¹⁰³(104-digit number)
29541475255786511168…82419864385134795841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.908 Γ— 10¹⁰³(104-digit number)
59082950511573022337…64839728770269591681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.181 Γ— 10¹⁰⁴(105-digit number)
11816590102314604467…29679457540539183361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.363 Γ— 10¹⁰⁴(105-digit number)
23633180204629208934…59358915081078366721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.726 Γ— 10¹⁰⁴(105-digit number)
47266360409258417869…18717830162156733441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.453 Γ— 10¹⁰⁴(105-digit number)
94532720818516835739…37435660324313466881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.890 Γ— 10¹⁰⁡(106-digit number)
18906544163703367147…74871320648626933761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.781 Γ— 10¹⁰⁡(106-digit number)
37813088327406734295…49742641297253867521
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 59482

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock cce3f559b720d639b9ca50ad97f26ff967fe4bd498314ed7cbbeea8c88f6dc72

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #59,482 on Chainz β†—
Circulating Supply:57,857,994 XPMΒ·at block #6,826,729 Β· updates every 60s
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