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Block #272,383

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/25/2013, 5:45:17 AM Β· Difficulty 9.9527 Β· 6,552,543 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e80ec97bb2a1fe4b4fae795af37bb41a4496192d67c293812acfd0ca5835fb7d
View on Chainz β†—

Height

#272,383

Difficulty

9.952695

Transactions

1

Size

199 B

Version

2

Bits

09f3e3ce

Nonce

106,348

Timestamp

11/25/2013, 5:45:17 AM

Confirmations

6,552,543

Merkle Root

f37c311d0d1b3bc808567531104169805f4288f4a1f009869be4296b6429dc12
Transactions (1)
Coinbasef37c311d0d1b3b…e4296b6429dc12
1 in β†’ 1 out10.0800 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.

1.917 Γ— 10⁹¹(92-digit number)
19174492448498136556…11433360497839856000
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
1.917 Γ— 10⁹¹(92-digit number)
19174492448498136556…11433360497839856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.834 Γ— 10⁹¹(92-digit number)
38348984896996273112…22866720995679712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.669 Γ— 10⁹¹(92-digit number)
76697969793992546224…45733441991359424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.533 Γ— 10⁹²(93-digit number)
15339593958798509244…91466883982718848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.067 Γ— 10⁹²(93-digit number)
30679187917597018489…82933767965437696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.135 Γ— 10⁹²(93-digit number)
61358375835194036979…65867535930875392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.227 Γ— 10⁹³(94-digit number)
12271675167038807395…31735071861750784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.454 Γ— 10⁹³(94-digit number)
24543350334077614791…63470143723501568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.908 Γ— 10⁹³(94-digit number)
49086700668155229583…26940287447003136001
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 272383

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 e80ec97bb2a1fe4b4fae795af37bb41a4496192d67c293812acfd0ca5835fb7d

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 #272,383 on Chainz β†—
Circulating Supply:57,843,484 XPMΒ·at block #6,824,925 Β· updates every 60s
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