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Block #306,642

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/12/2013, 4:07:43 AM Β· Difficulty 9.9939 Β· 6,494,753 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ff56b0ea54b9dc37a16686bab6bb8005b5b7dc0170219aeac34b3f4fe5fcf67d
View on Chainz β†—

Height

#306,642

Difficulty

9.993937

Transactions

1

Size

201 B

Version

2

Bits

09fe72a8

Nonce

324,584

Timestamp

12/12/2013, 4:07:43 AM

Confirmations

6,494,753

Merkle Root

68d33167f9ec14deb1757d2f35dc1435f10eae30980fda76c4016c7f3daf2649
Transactions (1)
Coinbase68d33167f9ec14…016c7f3daf2649
1 in β†’ 1 out10.0000 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.

8.052 Γ— 10⁹⁢(97-digit number)
80529578569745170874…60010359874536475680
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
8.052 Γ— 10⁹⁢(97-digit number)
80529578569745170874…60010359874536475681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.610 Γ— 10⁹⁷(98-digit number)
16105915713949034174…20020719749072951361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.221 Γ— 10⁹⁷(98-digit number)
32211831427898068349…40041439498145902721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.442 Γ— 10⁹⁷(98-digit number)
64423662855796136699…80082878996291805441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.288 Γ— 10⁹⁸(99-digit number)
12884732571159227339…60165757992583610881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.576 Γ— 10⁹⁸(99-digit number)
25769465142318454679…20331515985167221761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.153 Γ— 10⁹⁸(99-digit number)
51538930284636909359…40663031970334443521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.030 Γ— 10⁹⁹(100-digit number)
10307786056927381871…81326063940668887041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.061 Γ— 10⁹⁹(100-digit number)
20615572113854763743…62652127881337774081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.123 Γ— 10⁹⁹(100-digit number)
41231144227709527487…25304255762675548161
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 306642

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 ff56b0ea54b9dc37a16686bab6bb8005b5b7dc0170219aeac34b3f4fe5fcf67d

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 #306,642 on Chainz β†—
Circulating Supply:57,655,227 XPMΒ·at block #6,801,394 Β· updates every 60s
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