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Block #265,391

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2013, 12:50:47 PM Β· Difficulty 9.9626 Β· 6,571,639 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d07fd17724cb84bf61086fffdf618cb096a64c235ac53b9b9cb3ec084b028eed
View on Chainz β†—

Height

#265,391

Difficulty

9.962649

Transactions

1

Size

227 B

Version

2

Bits

09f67028

Nonce

12,033

Timestamp

11/19/2013, 12:50:47 PM

Confirmations

6,571,639

Merkle Root

8cf2e31308a91fc31e758c23b996cd411e523b26e3f3cf159001504ef9d91866
Transactions (1)
Coinbase8cf2e31308a91f…01504ef9d91866
1 in β†’ 2 out10.0600 XPM137 B
AKcbk49N…GJbKa7j1ALfEGCwh…VawujfMm
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.

7.800 Γ— 10⁹⁡(96-digit number)
78009180806343574321…64181921545269714560
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
7.800 Γ— 10⁹⁡(96-digit number)
78009180806343574321…64181921545269714561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.560 Γ— 10⁹⁢(97-digit number)
15601836161268714864…28363843090539429121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.120 Γ— 10⁹⁢(97-digit number)
31203672322537429728…56727686181078858241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.240 Γ— 10⁹⁢(97-digit number)
62407344645074859457…13455372362157716481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.248 Γ— 10⁹⁷(98-digit number)
12481468929014971891…26910744724315432961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.496 Γ— 10⁹⁷(98-digit number)
24962937858029943782…53821489448630865921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.992 Γ— 10⁹⁷(98-digit number)
49925875716059887565…07642978897261731841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.985 Γ— 10⁹⁷(98-digit number)
99851751432119775131…15285957794523463681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.997 Γ— 10⁹⁸(99-digit number)
19970350286423955026…30571915589046927361
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 265391

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 d07fd17724cb84bf61086fffdf618cb096a64c235ac53b9b9cb3ec084b028eed

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 #265,391 on Chainz β†—
Circulating Supply:57,940,540 XPMΒ·at block #6,837,029 Β· updates every 60s
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