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Home/Chain Registry/Block #1,806,401

Block #1,806,401

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2016, 12:06:56 PM Β· Difficulty 10.8244 Β· 5,035,686 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
89fcd2f381e7396d209d427ca7ffe90cf62bb91d8e9a13a0793524d81b652ec1
View on Chainz β†—

Difficulty

10.824420

Transactions

1

Size

201 B

Version

2

Bits

0ad30d2f

Nonce

181,508,172

Timestamp

10/13/2016, 12:06:56 PM

Confirmations

5,035,686

Merkle Root

fa4e269425a71a96754f70f87cbeaf46ba450b2f37646917ac7f486a5d3fe66e
Transactions (1)
Coinbasefa4e269425a71a…7f486a5d3fe66e
1 in β†’ 1 out8.5200 XPM110 B
AZivDVSq…HSbUxvCB
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.

1.241 Γ— 10⁹⁢(97-digit number)
12414533399225144052…18047595652805580800
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
1.241 Γ— 10⁹⁢(97-digit number)
12414533399225144052…18047595652805580799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.482 Γ— 10⁹⁢(97-digit number)
24829066798450288104…36095191305611161599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.965 Γ— 10⁹⁢(97-digit number)
49658133596900576208…72190382611222323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.931 Γ— 10⁹⁢(97-digit number)
99316267193801152416…44380765222444646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.986 Γ— 10⁹⁷(98-digit number)
19863253438760230483…88761530444889292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.972 Γ— 10⁹⁷(98-digit number)
39726506877520460966…77523060889778585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.945 Γ— 10⁹⁷(98-digit number)
79453013755040921932…55046121779557171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.589 Γ— 10⁹⁸(99-digit number)
15890602751008184386…10092243559114342399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.178 Γ— 10⁹⁸(99-digit number)
31781205502016368773…20184487118228684799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.356 Γ— 10⁹⁸(99-digit number)
63562411004032737546…40368974236457369599
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 1806401

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 89fcd2f381e7396d209d427ca7ffe90cf62bb91d8e9a13a0793524d81b652ec1

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 #1,806,401 on Chainz β†—
Circulating Supply:57,981,081 XPMΒ·at block #6,842,086 Β· updates every 60s
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