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Home/Chain Registry/Block #2,947,444

Block #2,947,444

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/1/2018, 2:52:10 PM Β· Difficulty 11.3920 Β· 3,895,150 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8b3ea001ad98fab781efcb66ea9d9cb37e1e7273f02f5fc9be8f59d44b76c004
View on Chainz β†—

Difficulty

11.392043

Transactions

1

Size

200 B

Version

2

Bits

0b645cf1

Nonce

168,443,065

Timestamp

12/1/2018, 2:52:10 PM

Confirmations

3,895,150

Merkle Root

ce05a554867c11cfbc024d3a4141ff48f8e21f09af080725e4c2becec769ea1b
Transactions (1)
Coinbasece05a554867c11…c2becec769ea1b
1 in β†’ 1 out7.6900 XPM110 B
AUhjokok…k5m93PZR
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.

7.994 Γ— 10⁹³(94-digit number)
79941373110567023476…97947221230249847040
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
7.994 Γ— 10⁹³(94-digit number)
79941373110567023476…97947221230249847041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.598 Γ— 10⁹⁴(95-digit number)
15988274622113404695…95894442460499694081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.197 Γ— 10⁹⁴(95-digit number)
31976549244226809390…91788884920999388161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.395 Γ— 10⁹⁴(95-digit number)
63953098488453618781…83577769841998776321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.279 Γ— 10⁹⁡(96-digit number)
12790619697690723756…67155539683997552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.558 Γ— 10⁹⁡(96-digit number)
25581239395381447512…34311079367995105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.116 Γ— 10⁹⁡(96-digit number)
51162478790762895025…68622158735990210561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.023 Γ— 10⁹⁢(97-digit number)
10232495758152579005…37244317471980421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.046 Γ— 10⁹⁢(97-digit number)
20464991516305158010…74488634943960842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.092 Γ— 10⁹⁢(97-digit number)
40929983032610316020…48977269887921684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.185 Γ— 10⁹⁢(97-digit number)
81859966065220632040…97954539775843368961
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 2947444

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 8b3ea001ad98fab781efcb66ea9d9cb37e1e7273f02f5fc9be8f59d44b76c004

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 #2,947,444 on Chainz β†—
Circulating Supply:57,985,182 XPMΒ·at block #6,842,593 Β· updates every 60s
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