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Block #58,604

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2013, 9:37:39 PM Β· Difficulty 8.9608 Β· 6,749,518 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ec3e54688222aa2f9e930501730ddff8b6f5782c009745a6e1b3daf8bf8a7dc9
View on Chainz β†—

Height

#58,604

Difficulty

8.960767

Transactions

1

Size

199 B

Version

2

Bits

08f5f4ce

Nonce

1

Timestamp

7/17/2013, 9:37:39 PM

Confirmations

6,749,518

Merkle Root

5446334d552df29cdd60598de962a3add8ca0b3f5fb3c055ac14cb5cf812f5a3
Transactions (1)
Coinbase5446334d552df2…14cb5cf812f5a3
1 in β†’ 1 out12.4400 XPM110 B
AYCQsY6D…sFr8Cxp5
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.

1.011 Γ— 10⁹¹(92-digit number)
10113225857888059369…21127409391514796420
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
1.011 Γ— 10⁹¹(92-digit number)
10113225857888059369…21127409391514796421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.022 Γ— 10⁹¹(92-digit number)
20226451715776118738…42254818783029592841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.045 Γ— 10⁹¹(92-digit number)
40452903431552237477…84509637566059185681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.090 Γ— 10⁹¹(92-digit number)
80905806863104474955…69019275132118371361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.618 Γ— 10⁹²(93-digit number)
16181161372620894991…38038550264236742721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.236 Γ— 10⁹²(93-digit number)
32362322745241789982…76077100528473485441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.472 Γ— 10⁹²(93-digit number)
64724645490483579964…52154201056946970881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.294 Γ— 10⁹³(94-digit number)
12944929098096715992…04308402113893941761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 58604

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 ec3e54688222aa2f9e930501730ddff8b6f5782c009745a6e1b3daf8bf8a7dc9

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 #58,604 on Chainz β†—
Circulating Supply:57,709,016 XPMΒ·at block #6,808,121 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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