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Block #67,730

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 12:29:34 AM Β· Difficulty 8.9884 Β· 6,731,420 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7b5ef996117bd29d969522e62d58ad7772f82589952e6f8d21fc08f4e86ac2a9
View on Chainz β†—

Height

#67,730

Difficulty

8.988409

Transactions

1

Size

199 B

Version

2

Bits

08fd085d

Nonce

735

Timestamp

7/20/2013, 12:29:34 AM

Confirmations

6,731,420

Merkle Root

448ec773cf97b7a94a159934339cd9714546dcb830e18b94cba412420bc71959
Transactions (1)
Coinbase448ec773cf97b7…a412420bc71959
1 in β†’ 1 out12.3600 XPM110 B
AQfNHxHX…A14bzmWx
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.

2.101 Γ— 10⁹³(94-digit number)
21016310468549367559…43541197149162173740
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
2.101 Γ— 10⁹³(94-digit number)
21016310468549367559…43541197149162173741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.203 Γ— 10⁹³(94-digit number)
42032620937098735119…87082394298324347481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.406 Γ— 10⁹³(94-digit number)
84065241874197470238…74164788596648694961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.681 Γ— 10⁹⁴(95-digit number)
16813048374839494047…48329577193297389921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.362 Γ— 10⁹⁴(95-digit number)
33626096749678988095…96659154386594779841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.725 Γ— 10⁹⁴(95-digit number)
67252193499357976190…93318308773189559681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.345 Γ— 10⁹⁡(96-digit number)
13450438699871595238…86636617546379119361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.690 Γ— 10⁹⁡(96-digit number)
26900877399743190476…73273235092758238721
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 67730

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 7b5ef996117bd29d969522e62d58ad7772f82589952e6f8d21fc08f4e86ac2a9

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 #67,730 on Chainz β†—
Circulating Supply:57,637,235 XPMΒ·at block #6,799,149 Β· updates every 60s
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