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Home/Chain Registry/Block #284,839

Block #284,839

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2013, 6:51:53 AM Β· Difficulty 9.9833 Β· 6,546,856 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
308066676b072e9a88488dd4c7186a9ee9595e72f108360f7322c9afe58e428e
View on Chainz β†—

Height

#284,839

Difficulty

9.983349

Transactions

1

Size

209 B

Version

2

Bits

09fbbcbf

Nonce

9,795

Timestamp

11/30/2013, 6:51:53 AM

Confirmations

6,546,856

Merkle Root

9a1cd7934173f655b47ca6ba392a2c3766ae3426e0692f233cb770e601feb523
Transactions (1)
Coinbase9a1cd7934173f6…b770e601feb523
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.

3.274 Γ— 10¹⁰²(103-digit number)
32743640388346640548…76171752054127088470
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
3.274 Γ— 10¹⁰²(103-digit number)
32743640388346640548…76171752054127088471
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.548 Γ— 10¹⁰²(103-digit number)
65487280776693281097…52343504108254176941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.309 Γ— 10¹⁰³(104-digit number)
13097456155338656219…04687008216508353881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.619 Γ— 10¹⁰³(104-digit number)
26194912310677312439…09374016433016707761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.238 Γ— 10¹⁰³(104-digit number)
52389824621354624878…18748032866033415521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.047 Γ— 10¹⁰⁴(105-digit number)
10477964924270924975…37496065732066831041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.095 Γ— 10¹⁰⁴(105-digit number)
20955929848541849951…74992131464133662081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.191 Γ— 10¹⁰⁴(105-digit number)
41911859697083699902…49984262928267324161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.382 Γ— 10¹⁰⁴(105-digit number)
83823719394167399804…99968525856534648321
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 284839

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 308066676b072e9a88488dd4c7186a9ee9595e72f108360f7322c9afe58e428e

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 #284,839 on Chainz β†—
Circulating Supply:57,897,668 XPMΒ·at block #6,831,694 Β· updates every 60s
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