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Block #470,908

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/2/2014, 6:07:13 AM Β· Difficulty 10.4297 Β· 6,329,455 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e839ea5cf71882fcaa5a740c31ab327c92c3cdc21a0ba1bf66b4f2bf8d900f73
View on Chainz β†—

Height

#470,908

Difficulty

10.429717

Transactions

1

Size

203 B

Version

2

Bits

0a6e01e8

Nonce

421,574

Timestamp

4/2/2014, 6:07:13 AM

Confirmations

6,329,455

Merkle Root

1a15fa8ea9a9e24b6e1b3d664f942befd08c0fb485f60df990bc5f4cd6daf7a1
Transactions (1)
Coinbase1a15fa8ea9a9e2…bc5f4cd6daf7a1
1 in β†’ 1 out9.1800 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.174 Γ— 10¹⁰²(103-digit number)
11740047260414631102…84731795468795151680
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
1.174 Γ— 10¹⁰²(103-digit number)
11740047260414631102…84731795468795151681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.348 Γ— 10¹⁰²(103-digit number)
23480094520829262205…69463590937590303361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.696 Γ— 10¹⁰²(103-digit number)
46960189041658524410…38927181875180606721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.392 Γ— 10¹⁰²(103-digit number)
93920378083317048820…77854363750361213441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.878 Γ— 10¹⁰³(104-digit number)
18784075616663409764…55708727500722426881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.756 Γ— 10¹⁰³(104-digit number)
37568151233326819528…11417455001444853761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.513 Γ— 10¹⁰³(104-digit number)
75136302466653639056…22834910002889707521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.502 Γ— 10¹⁰⁴(105-digit number)
15027260493330727811…45669820005779415041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.005 Γ— 10¹⁰⁴(105-digit number)
30054520986661455622…91339640011558830081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.010 Γ— 10¹⁰⁴(105-digit number)
60109041973322911245…82679280023117660161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 470908

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 e839ea5cf71882fcaa5a740c31ab327c92c3cdc21a0ba1bf66b4f2bf8d900f73

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 #470,908 on Chainz β†—
Circulating Supply:57,646,962 XPMΒ·at block #6,800,362 Β· updates every 60s
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