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Home/Chain Registry/Block #1,811,257

Block #1,811,257

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/17/2016, 1:03:25 PM Β· Difficulty 10.7878 Β· 5,031,350 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8e224e324ce1a6c6a6ea227f321ec701de1878852ba34c049c8687ee0469f8ac
View on Chainz β†—

Difficulty

10.787755

Transactions

1

Size

200 B

Version

2

Bits

0ac9aa57

Nonce

104,449,935

Timestamp

10/17/2016, 1:03:25 PM

Confirmations

5,031,350

Merkle Root

cc2760cbf7326fe16e3cf0d1e7d316de81262512fb1e89ae01e309bc979c2f2b
Transactions (1)
Coinbasecc2760cbf7326f…e309bc979c2f2b
1 in β†’ 1 out8.5800 XPM110 B
APzLpsSF…2nbuM7L3
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.

5.711 Γ— 10⁹⁡(96-digit number)
57111529420753240593…00431198324013301760
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.711 Γ— 10⁹⁡(96-digit number)
57111529420753240593…00431198324013301759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.142 Γ— 10⁹⁢(97-digit number)
11422305884150648118…00862396648026603519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.284 Γ— 10⁹⁢(97-digit number)
22844611768301296237…01724793296053207039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.568 Γ— 10⁹⁢(97-digit number)
45689223536602592474…03449586592106414079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.137 Γ— 10⁹⁢(97-digit number)
91378447073205184949…06899173184212828159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.827 Γ— 10⁹⁷(98-digit number)
18275689414641036989…13798346368425656319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.655 Γ— 10⁹⁷(98-digit number)
36551378829282073979…27596692736851312639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.310 Γ— 10⁹⁷(98-digit number)
73102757658564147959…55193385473702625279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.462 Γ— 10⁹⁸(99-digit number)
14620551531712829591…10386770947405250559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.924 Γ— 10⁹⁸(99-digit number)
29241103063425659183…20773541894810501119
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 1811257

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 8e224e324ce1a6c6a6ea227f321ec701de1878852ba34c049c8687ee0469f8ac

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 #1,811,257 on Chainz β†—
Circulating Supply:57,985,285 XPMΒ·at block #6,842,606 Β· updates every 60s
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