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Block #322,627

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/21/2013, 3:14:43 AM Β· Difficulty 10.1955 Β· 6,503,525 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b4c02b677022119fedcf9281c4e3c1e3ce9e0c8d26ccbc485adbd241911fb0b1
View on Chainz β†—

Height

#322,627

Difficulty

10.195470

Transactions

1

Size

205 B

Version

2

Bits

0a320a4f

Nonce

21,213

Timestamp

12/21/2013, 3:14:43 AM

Confirmations

6,503,525

Merkle Root

2150242ccb73c4f8768c259875ffe61454941be3c17a011b68f2d9858e0731bb
Transactions (1)
Coinbase2150242ccb73c4…f2d9858e0731bb
1 in β†’ 1 out9.6100 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.

7.656 Γ— 10⁹²(93-digit number)
76562762403637720712…27099449293910246400
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
7.656 Γ— 10⁹²(93-digit number)
76562762403637720712…27099449293910246401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.531 Γ— 10⁹³(94-digit number)
15312552480727544142…54198898587820492801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.062 Γ— 10⁹³(94-digit number)
30625104961455088285…08397797175640985601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.125 Γ— 10⁹³(94-digit number)
61250209922910176570…16795594351281971201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.225 Γ— 10⁹⁴(95-digit number)
12250041984582035314…33591188702563942401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.450 Γ— 10⁹⁴(95-digit number)
24500083969164070628…67182377405127884801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.900 Γ— 10⁹⁴(95-digit number)
49000167938328141256…34364754810255769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.800 Γ— 10⁹⁴(95-digit number)
98000335876656282512…68729509620511539201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.960 Γ— 10⁹⁡(96-digit number)
19600067175331256502…37459019241023078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.920 Γ— 10⁹⁡(96-digit number)
39200134350662513004…74918038482046156801
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 322627

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 b4c02b677022119fedcf9281c4e3c1e3ce9e0c8d26ccbc485adbd241911fb0b1

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 #322,627 on Chainz β†—
Circulating Supply:57,853,342 XPMΒ·at block #6,826,151 Β· updates every 60s
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