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Home/Chain Registry/Block #3,031,227

Block #3,031,227

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/30/2019, 5:00:55 AM Β· Difficulty 11.0959 Β· 3,810,650 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e5168a43f9bf6bf8a4120485b6eb712b77fddbb49ee5e36f2327defe53ffabde
View on Chainz β†—

Difficulty

11.095922

Transactions

1

Size

200 B

Version

2

Bits

0b188e50

Nonce

833,146,007

Timestamp

1/30/2019, 5:00:55 AM

Confirmations

3,810,650

Merkle Root

41143b2501cb62707c426b1cdae1972d4b4ea9b30cbdcb89f54072e3de7a7021
Transactions (1)
Coinbase41143b2501cb62…4072e3de7a7021
1 in β†’ 1 out8.1100 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.137 Γ— 10⁹⁡(96-digit number)
11370812280844721824…74042255501954630540
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
1.137 Γ— 10⁹⁡(96-digit number)
11370812280844721824…74042255501954630541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.274 Γ— 10⁹⁡(96-digit number)
22741624561689443648…48084511003909261081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.548 Γ— 10⁹⁡(96-digit number)
45483249123378887296…96169022007818522161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.096 Γ— 10⁹⁡(96-digit number)
90966498246757774592…92338044015637044321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.819 Γ— 10⁹⁢(97-digit number)
18193299649351554918…84676088031274088641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.638 Γ— 10⁹⁢(97-digit number)
36386599298703109837…69352176062548177281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.277 Γ— 10⁹⁢(97-digit number)
72773198597406219674…38704352125096354561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.455 Γ— 10⁹⁷(98-digit number)
14554639719481243934…77408704250192709121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.910 Γ— 10⁹⁷(98-digit number)
29109279438962487869…54817408500385418241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.821 Γ— 10⁹⁷(98-digit number)
58218558877924975739…09634817000770836481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.164 Γ— 10⁹⁸(99-digit number)
11643711775584995147…19269634001541672961
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 3031227

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 e5168a43f9bf6bf8a4120485b6eb712b77fddbb49ee5e36f2327defe53ffabde

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 #3,031,227 on Chainz β†—
Circulating Supply:57,979,392 XPMΒ·at block #6,841,876 Β· updates every 60s
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