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Home/Chain Registry/Block #2,944,164

Block #2,944,164

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/29/2018, 7:25:37 AM Β· Difficulty 11.3975 Β· 3,889,750 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
be47b593cdf00f2bf9b3944b1019b0d36e60afa7f2c6dab1f8090870b07be376
View on Chainz β†—

Difficulty

11.397470

Transactions

1

Size

201 B

Version

2

Bits

0b65c090

Nonce

1,632,199,504

Timestamp

11/29/2018, 7:25:37 AM

Confirmations

3,889,750

Merkle Root

c5fd2961a578da306fedbb2c3d6e2b66fe4800ab8515332114a7c659a40e204f
Transactions (1)
Coinbasec5fd2961a578da…a7c659a40e204f
1 in β†’ 1 out7.6900 XPM110 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.

3.324 Γ— 10⁹⁢(97-digit number)
33248275416424794094…04242742545594419200
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
3.324 Γ— 10⁹⁢(97-digit number)
33248275416424794094…04242742545594419201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.649 Γ— 10⁹⁢(97-digit number)
66496550832849588189…08485485091188838401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.329 Γ— 10⁹⁷(98-digit number)
13299310166569917637…16970970182377676801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.659 Γ— 10⁹⁷(98-digit number)
26598620333139835275…33941940364755353601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.319 Γ— 10⁹⁷(98-digit number)
53197240666279670551…67883880729510707201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.063 Γ— 10⁹⁸(99-digit number)
10639448133255934110…35767761459021414401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.127 Γ— 10⁹⁸(99-digit number)
21278896266511868220…71535522918042828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.255 Γ— 10⁹⁸(99-digit number)
42557792533023736441…43071045836085657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.511 Γ— 10⁹⁸(99-digit number)
85115585066047472883…86142091672171315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.702 Γ— 10⁹⁹(100-digit number)
17023117013209494576…72284183344342630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.404 Γ— 10⁹⁹(100-digit number)
34046234026418989153…44568366688685260801
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 2944164

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 be47b593cdf00f2bf9b3944b1019b0d36e60afa7f2c6dab1f8090870b07be376

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 #2,944,164 on Chainz β†—
Circulating Supply:57,915,538 XPMΒ·at block #6,833,913 Β· updates every 60s
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