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Home/Chain Registry/Block #4,010,266

Block #4,010,266

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/27/2020, 9:55:23 AM Β· Difficulty 10.8480 Β· 2,822,234 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6cab96d87dbe5d31762d6d4df3dde242bc1c6c499924f929550985285ab33a46
View on Chainz β†—

Difficulty

10.848037

Transactions

1

Size

200 B

Version

2

Bits

0ad918ee

Nonce

42,088,355

Timestamp

12/27/2020, 9:55:23 AM

Confirmations

2,822,234

Merkle Root

712c1236d203ba907645beb337153a01bb08f8aa56c7c7097b3ec7ca3891822e
Transactions (1)
Coinbase712c1236d203ba…3ec7ca3891822e
1 in β†’ 1 out8.4800 XPM109 B
ASiq2qtK…VMhmk7yL
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.

4.211 Γ— 10⁹⁢(97-digit number)
42111803288827820427…79122994428267714560
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
4.211 Γ— 10⁹⁢(97-digit number)
42111803288827820427…79122994428267714561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.422 Γ— 10⁹⁢(97-digit number)
84223606577655640855…58245988856535429121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.684 Γ— 10⁹⁷(98-digit number)
16844721315531128171…16491977713070858241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.368 Γ— 10⁹⁷(98-digit number)
33689442631062256342…32983955426141716481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.737 Γ— 10⁹⁷(98-digit number)
67378885262124512684…65967910852283432961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.347 Γ— 10⁹⁸(99-digit number)
13475777052424902536…31935821704566865921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.695 Γ— 10⁹⁸(99-digit number)
26951554104849805073…63871643409133731841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.390 Γ— 10⁹⁸(99-digit number)
53903108209699610147…27743286818267463681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.078 Γ— 10⁹⁹(100-digit number)
10780621641939922029…55486573636534927361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.156 Γ— 10⁹⁹(100-digit number)
21561243283879844058…10973147273069854721
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 4010266

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 6cab96d87dbe5d31762d6d4df3dde242bc1c6c499924f929550985285ab33a46

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 #4,010,266 on Chainz β†—
Circulating Supply:57,904,157 XPMΒ·at block #6,832,499 Β· updates every 60s
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