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Block #482,640

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/9/2014, 2:47:02 PM Β· Difficulty 10.5487 Β· 6,314,798 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
71102cb6c0f7fd8c390cfdadfc37f54cd766207071e0c9603a1e6df70e81ba8c
View on Chainz β†—

Height

#482,640

Difficulty

10.548748

Transactions

1

Size

207 B

Version

2

Bits

0a8c7ac6

Nonce

28,367

Timestamp

4/9/2014, 2:47:02 PM

Confirmations

6,314,798

Merkle Root

fca6593cccb2657eb53f3bcd473f442314c4dc1321914db727e32d9d018293ea
Transactions (1)
Coinbasefca6593cccb265…e32d9d018293ea
1 in β†’ 1 out8.9700 XPM116 B
AbwWkWZt…kawDhufa
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.

2.844 Γ— 10⁹⁷(98-digit number)
28443664987265350570…17867127527839564720
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
2.844 Γ— 10⁹⁷(98-digit number)
28443664987265350570…17867127527839564721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.688 Γ— 10⁹⁷(98-digit number)
56887329974530701140…35734255055679129441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.137 Γ— 10⁹⁸(99-digit number)
11377465994906140228…71468510111358258881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.275 Γ— 10⁹⁸(99-digit number)
22754931989812280456…42937020222716517761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.550 Γ— 10⁹⁸(99-digit number)
45509863979624560912…85874040445433035521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.101 Γ— 10⁹⁸(99-digit number)
91019727959249121825…71748080890866071041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.820 Γ— 10⁹⁹(100-digit number)
18203945591849824365…43496161781732142081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.640 Γ— 10⁹⁹(100-digit number)
36407891183699648730…86992323563464284161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.281 Γ— 10⁹⁹(100-digit number)
72815782367399297460…73984647126928568321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.456 Γ— 10¹⁰⁰(101-digit number)
14563156473479859492…47969294253857136641
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 482640

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 71102cb6c0f7fd8c390cfdadfc37f54cd766207071e0c9603a1e6df70e81ba8c

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 #482,640 on Chainz β†—
Circulating Supply:57,623,532 XPMΒ·at block #6,797,437 Β· updates every 60s
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