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Block #72,314

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 11:24:34 PM Β· Difficulty 8.9940 Β· 6,724,114 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
644eb2375840d848e5a2fac4a246c71f6cacb41bbcbf450119d02821a4d35ad4
View on Chainz β†—

Height

#72,314

Difficulty

8.993970

Transactions

1

Size

201 B

Version

2

Bits

08fe74d1

Nonce

1,407

Timestamp

7/20/2013, 11:24:34 PM

Confirmations

6,724,114

Merkle Root

813665e31b98f0778a906dffc69e32029445578cca34ceeb5a8a3e6cde7c1405
Transactions (1)
Coinbase813665e31b98f0…8a3e6cde7c1405
1 in β†’ 1 out12.3400 XPM110 B
AL9bd3w8…rV2im3h8
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.

7.572 Γ— 10⁹⁡(96-digit number)
75724278891415504775…93764976306995617670
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
7.572 Γ— 10⁹⁡(96-digit number)
75724278891415504775…93764976306995617671
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.514 Γ— 10⁹⁢(97-digit number)
15144855778283100955…87529952613991235341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.028 Γ— 10⁹⁢(97-digit number)
30289711556566201910…75059905227982470681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.057 Γ— 10⁹⁢(97-digit number)
60579423113132403820…50119810455964941361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.211 Γ— 10⁹⁷(98-digit number)
12115884622626480764…00239620911929882721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.423 Γ— 10⁹⁷(98-digit number)
24231769245252961528…00479241823859765441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.846 Γ— 10⁹⁷(98-digit number)
48463538490505923056…00958483647719530881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.692 Γ— 10⁹⁷(98-digit number)
96927076981011846112…01916967295439061761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.938 Γ— 10⁹⁸(99-digit number)
19385415396202369222…03833934590878123521
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 72314

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 644eb2375840d848e5a2fac4a246c71f6cacb41bbcbf450119d02821a4d35ad4

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 #72,314 on Chainz β†—
Circulating Supply:57,615,414 XPMΒ·at block #6,796,427 Β· updates every 60s
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