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Home/Chain Registry/Block #3,004,871

Block #3,004,871

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/11/2019, 11:01:19 AM Β· Difficulty 11.2031 Β· 3,839,225 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c3d69b25cff4f8362c00b020d1889e1c7b2a3f0190e3d5caaaa99202beccc2a4
View on Chainz β†—

Difficulty

11.203081

Transactions

1

Size

199 B

Version

2

Bits

0b33fd1f

Nonce

1,889,361,714

Timestamp

1/11/2019, 11:01:19 AM

Confirmations

3,839,225

Merkle Root

d6c63441793bf24963a3700e49d5aa85875c8da83f3018f5745ffa238d933e64
Transactions (1)
Coinbased6c63441793bf2…5ffa238d933e64
1 in β†’ 1 out7.9500 XPM109 B
AbXwmGxD…4XXYP765
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.

1.822 Γ— 10⁹⁴(95-digit number)
18220322917439268221…58086685441116640960
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
1.822 Γ— 10⁹⁴(95-digit number)
18220322917439268221…58086685441116640961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.644 Γ— 10⁹⁴(95-digit number)
36440645834878536443…16173370882233281921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.288 Γ— 10⁹⁴(95-digit number)
72881291669757072886…32346741764466563841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.457 Γ— 10⁹⁡(96-digit number)
14576258333951414577…64693483528933127681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.915 Γ— 10⁹⁡(96-digit number)
29152516667902829154…29386967057866255361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.830 Γ— 10⁹⁡(96-digit number)
58305033335805658308…58773934115732510721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.166 Γ— 10⁹⁢(97-digit number)
11661006667161131661…17547868231465021441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.332 Γ— 10⁹⁢(97-digit number)
23322013334322263323…35095736462930042881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.664 Γ— 10⁹⁢(97-digit number)
46644026668644526647…70191472925860085761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.328 Γ— 10⁹⁢(97-digit number)
93288053337289053294…40382945851720171521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.865 Γ— 10⁹⁷(98-digit number)
18657610667457810658…80765891703440343041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3004871

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 c3d69b25cff4f8362c00b020d1889e1c7b2a3f0190e3d5caaaa99202beccc2a4

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 #3,004,871 on Chainz β†—
Circulating Supply:57,997,142 XPMΒ·at block #6,844,095 Β· updates every 60s
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