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Block #62,456

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 7:28:51 PM Β· Difficulty 8.9764 Β· 6,737,805 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
59faf8fc6e2e5221494201f316b482734d5ddf8f7d32556488c400a94c55aa9c
View on Chainz β†—

Height

#62,456

Difficulty

8.976398

Transactions

1

Size

200 B

Version

2

Bits

08f9f530

Nonce

1,280

Timestamp

7/18/2013, 7:28:51 PM

Confirmations

6,737,805

Merkle Root

846b44fe25749c5ed72f668013142aa45b5b7b520369f76e23f0a4ec3b07f6eb
Transactions (1)
Coinbase846b44fe25749c…f0a4ec3b07f6eb
1 in β†’ 1 out12.3900 XPM110 B
AX5TJE28…uYocNWtF
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.

9.141 Γ— 10⁹⁴(95-digit number)
91419751476499893116…05610518360832978400
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
9.141 Γ— 10⁹⁴(95-digit number)
91419751476499893116…05610518360832978401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.828 Γ— 10⁹⁡(96-digit number)
18283950295299978623…11221036721665956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.656 Γ— 10⁹⁡(96-digit number)
36567900590599957246…22442073443331913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.313 Γ— 10⁹⁡(96-digit number)
73135801181199914493…44884146886663827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.462 Γ— 10⁹⁢(97-digit number)
14627160236239982898…89768293773327654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.925 Γ— 10⁹⁢(97-digit number)
29254320472479965797…79536587546655308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.850 Γ— 10⁹⁢(97-digit number)
58508640944959931594…59073175093310617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.170 Γ— 10⁹⁷(98-digit number)
11701728188991986318…18146350186621235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.340 Γ— 10⁹⁷(98-digit number)
23403456377983972637…36292700373242470401
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 62456

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 59faf8fc6e2e5221494201f316b482734d5ddf8f7d32556488c400a94c55aa9c

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 #62,456 on Chainz β†—
Circulating Supply:57,646,144 XPMΒ·at block #6,800,260 Β· updates every 60s
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