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Block #217,230

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/19/2013, 5:39:48 AM Β· Difficulty 9.9277 Β· 6,580,058 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ea6c9dec21551f0d864571797c5b4d4bf4d586903969f40d66f9562406906c0
View on Chainz β†—

Height

#217,230

Difficulty

9.927724

Transactions

1

Size

200 B

Version

2

Bits

09ed7f55

Nonce

32,965

Timestamp

10/19/2013, 5:39:48 AM

Confirmations

6,580,058

Merkle Root

9f00f907520adf9ea601c6222a0f6e920af2d99d475db7de589a51d17293786a
Transactions (1)
Coinbase9f00f907520adf…9a51d17293786a
1 in β†’ 1 out10.1300 XPM110 B
AbuU1HhS…JPwsJEbB
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.

1.356 Γ— 10⁹⁡(96-digit number)
13562357147853463620…34042141167018313760
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
1.356 Γ— 10⁹⁡(96-digit number)
13562357147853463620…34042141167018313761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.712 Γ— 10⁹⁡(96-digit number)
27124714295706927240…68084282334036627521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.424 Γ— 10⁹⁡(96-digit number)
54249428591413854480…36168564668073255041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.084 Γ— 10⁹⁢(97-digit number)
10849885718282770896…72337129336146510081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.169 Γ— 10⁹⁢(97-digit number)
21699771436565541792…44674258672293020161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.339 Γ— 10⁹⁢(97-digit number)
43399542873131083584…89348517344586040321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.679 Γ— 10⁹⁢(97-digit number)
86799085746262167168…78697034689172080641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.735 Γ— 10⁹⁷(98-digit number)
17359817149252433433…57394069378344161281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.471 Γ— 10⁹⁷(98-digit number)
34719634298504866867…14788138756688322561
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 217230

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 6ea6c9dec21551f0d864571797c5b4d4bf4d586903969f40d66f9562406906c0

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 #217,230 on Chainz β†—
Circulating Supply:57,622,334 XPMΒ·at block #6,797,287 Β· updates every 60s
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