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Block #266,891

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/20/2013, 7:27:06 PM Β· Difficulty 9.9601 Β· 6,533,375 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
82b2db9c91d207cd7e151704913c86e2fc8d77fee5f5acd5860b6130b429522b
View on Chainz β†—

Height

#266,891

Difficulty

9.960126

Transactions

1

Size

207 B

Version

2

Bits

09f5cad7

Nonce

16,780,079

Timestamp

11/20/2013, 7:27:06 PM

Confirmations

6,533,375

Merkle Root

5c94bdae1e56e7e5e29af1a5e0d5bc5013bd8e66b9aa176b91c96f89d9ff3049
Transactions (1)
Coinbase5c94bdae1e56e7…c96f89d9ff3049
1 in β†’ 1 out10.0700 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.

4.733 Γ— 10⁹⁢(97-digit number)
47336384614410363069…10968197245297403040
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
4.733 Γ— 10⁹⁢(97-digit number)
47336384614410363069…10968197245297403041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.467 Γ— 10⁹⁢(97-digit number)
94672769228820726138…21936394490594806081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.893 Γ— 10⁹⁷(98-digit number)
18934553845764145227…43872788981189612161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.786 Γ— 10⁹⁷(98-digit number)
37869107691528290455…87745577962379224321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.573 Γ— 10⁹⁷(98-digit number)
75738215383056580910…75491155924758448641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.514 Γ— 10⁹⁸(99-digit number)
15147643076611316182…50982311849516897281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.029 Γ— 10⁹⁸(99-digit number)
30295286153222632364…01964623699033794561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.059 Γ— 10⁹⁸(99-digit number)
60590572306445264728…03929247398067589121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.211 Γ— 10⁹⁹(100-digit number)
12118114461289052945…07858494796135178241
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 266891

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 82b2db9c91d207cd7e151704913c86e2fc8d77fee5f5acd5860b6130b429522b

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 #266,891 on Chainz β†—
Circulating Supply:57,646,185 XPMΒ·at block #6,800,265 Β· updates every 60s
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