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Block #265,431

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2013, 1:33:52 PM Β· Difficulty 9.9626 Β· 6,550,426 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c48633df387e23d27f07bd93ddb3d74994ddcbc78426866d0665f72ed5b4e656
View on Chainz β†—

Height

#265,431

Difficulty

9.962631

Transactions

1

Size

198 B

Version

2

Bits

09f66f04

Nonce

385,627

Timestamp

11/19/2013, 1:33:52 PM

Confirmations

6,550,426

Merkle Root

a05b4419935baa617eec1c256eff1f8360df67b551f0cca7dc483813c4bda5d8
Transactions (1)
Coinbasea05b4419935baa…483813c4bda5d8
1 in β†’ 1 out10.0600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

7.036 Γ— 10⁸⁹(90-digit number)
70367489245260553323…23533015583566299050
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
7.036 Γ— 10⁸⁹(90-digit number)
70367489245260553323…23533015583566299051
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.407 Γ— 10⁹⁰(91-digit number)
14073497849052110664…47066031167132598101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.814 Γ— 10⁹⁰(91-digit number)
28146995698104221329…94132062334265196201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.629 Γ— 10⁹⁰(91-digit number)
56293991396208442659…88264124668530392401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.125 Γ— 10⁹¹(92-digit number)
11258798279241688531…76528249337060784801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.251 Γ— 10⁹¹(92-digit number)
22517596558483377063…53056498674121569601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.503 Γ— 10⁹¹(92-digit number)
45035193116966754127…06112997348243139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.007 Γ— 10⁹¹(92-digit number)
90070386233933508254…12225994696486278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.801 Γ— 10⁹²(93-digit number)
18014077246786701650…24451989392972556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.602 Γ— 10⁹²(93-digit number)
36028154493573403301…48903978785945113601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 265431

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 c48633df387e23d27f07bd93ddb3d74994ddcbc78426866d0665f72ed5b4e656

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 #265,431 on Chainz β†—
Circulating Supply:57,770,967 XPMΒ·at block #6,815,856 Β· updates every 60s
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