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Block #284,339

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2013, 2:24:02 AM Β· Difficulty 9.9825 Β· 6,517,173 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c512d8a25f6ea1801bfb1259cd49949293a5cf9cd42a815362dcb634d16568ca
View on Chainz β†—

Height

#284,339

Difficulty

9.982543

Transactions

1

Size

208 B

Version

2

Bits

09fb87f5

Nonce

268,435,606

Timestamp

11/30/2013, 2:24:02 AM

Confirmations

6,517,173

Merkle Root

4645f994312e85260bd4ec05a5867ea1cfa0716167a51afad5f92938d833f2fa
Transactions (1)
Coinbase4645f994312e85…f92938d833f2fa
1 in β†’ 1 out10.0200 XPM116 B
AcLBm5Z9…S683d7c3
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.

3.214 Γ— 10⁹⁹(100-digit number)
32141538477380300145…81504021366980341760
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
3.214 Γ— 10⁹⁹(100-digit number)
32141538477380300145…81504021366980341761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.428 Γ— 10⁹⁹(100-digit number)
64283076954760600290…63008042733960683521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.285 Γ— 10¹⁰⁰(101-digit number)
12856615390952120058…26016085467921367041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.571 Γ— 10¹⁰⁰(101-digit number)
25713230781904240116…52032170935842734081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.142 Γ— 10¹⁰⁰(101-digit number)
51426461563808480232…04064341871685468161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.028 Γ— 10¹⁰¹(102-digit number)
10285292312761696046…08128683743370936321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.057 Γ— 10¹⁰¹(102-digit number)
20570584625523392092…16257367486741872641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.114 Γ— 10¹⁰¹(102-digit number)
41141169251046784185…32514734973483745281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.228 Γ— 10¹⁰¹(102-digit number)
82282338502093568371…65029469946967490561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.645 Γ— 10¹⁰²(103-digit number)
16456467700418713674…30058939893934981121
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 284339

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 c512d8a25f6ea1801bfb1259cd49949293a5cf9cd42a815362dcb634d16568ca

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 #284,339 on Chainz β†—
Circulating Supply:57,656,171 XPMΒ·at block #6,801,511 Β· updates every 60s
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