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Block #206,361

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2013, 6:22:34 PM Β· Difficulty 9.9010 Β· 6,606,487 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c4b71cee3876db393e3f4aaaa08cf6a750e1c2cc1c4a95e0b81ac383aef2f88e
View on Chainz β†—

Height

#206,361

Difficulty

9.900970

Transactions

1

Size

197 B

Version

2

Bits

09e6a5f8

Nonce

80,412

Timestamp

10/12/2013, 6:22:34 PM

Confirmations

6,606,487

Merkle Root

1120ae790aaf85a6fc71174499d7143f7b9d3cdba87e6e6ffb59f33c892f72fb
Transactions (1)
Coinbase1120ae790aaf85…59f33c892f72fb
1 in β†’ 1 out10.1900 XPM110 B
AFvfCa1W…3pZgbFWa
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.

3.179 Γ— 10⁸⁷(88-digit number)
31794330509100896357…48380614150440340480
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
3.179 Γ— 10⁸⁷(88-digit number)
31794330509100896357…48380614150440340481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.358 Γ— 10⁸⁷(88-digit number)
63588661018201792715…96761228300880680961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.271 Γ— 10⁸⁸(89-digit number)
12717732203640358543…93522456601761361921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.543 Γ— 10⁸⁸(89-digit number)
25435464407280717086…87044913203522723841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.087 Γ— 10⁸⁸(89-digit number)
50870928814561434172…74089826407045447681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.017 Γ— 10⁸⁹(90-digit number)
10174185762912286834…48179652814090895361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.034 Γ— 10⁸⁹(90-digit number)
20348371525824573668…96359305628181790721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.069 Γ— 10⁸⁹(90-digit number)
40696743051649147337…92718611256363581441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.139 Γ— 10⁸⁹(90-digit number)
81393486103298294675…85437222512727162881
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 206361

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 c4b71cee3876db393e3f4aaaa08cf6a750e1c2cc1c4a95e0b81ac383aef2f88e

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 #206,361 on Chainz β†—
Circulating Supply:57,746,819 XPMΒ·at block #6,812,847 Β· updates every 60s
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