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Home/Chain Registry/Block #2,812,128

Block #2,812,128

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2018, 11:32:30 AM Β· Difficulty 11.6686 Β· 4,024,548 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3eed165a0f1e6d54636821f44bd2e48831d8744df57af8f85bdf872981458bbd
View on Chainz β†—

Difficulty

11.668592

Transactions

1

Size

200 B

Version

2

Bits

0bab28d8

Nonce

229,801,966

Timestamp

8/27/2018, 11:32:30 AM

Confirmations

4,024,548

Merkle Root

2218354864cf4ffd0f02dadbe74c5857dae5e61ca07c9e241eeb3290c310ce38
Transactions (1)
Coinbase2218354864cf4f…eb3290c310ce38
1 in β†’ 1 out7.3300 XPM110 B
ANzjnyAD…rUQiALr4
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.

6.096 Γ— 10⁹³(94-digit number)
60962439359760252964…36478944434162936960
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
6.096 Γ— 10⁹³(94-digit number)
60962439359760252964…36478944434162936961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.219 Γ— 10⁹⁴(95-digit number)
12192487871952050592…72957888868325873921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.438 Γ— 10⁹⁴(95-digit number)
24384975743904101185…45915777736651747841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.876 Γ— 10⁹⁴(95-digit number)
48769951487808202371…91831555473303495681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.753 Γ— 10⁹⁴(95-digit number)
97539902975616404742…83663110946606991361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.950 Γ— 10⁹⁡(96-digit number)
19507980595123280948…67326221893213982721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.901 Γ— 10⁹⁡(96-digit number)
39015961190246561896…34652443786427965441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.803 Γ— 10⁹⁡(96-digit number)
78031922380493123793…69304887572855930881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.560 Γ— 10⁹⁢(97-digit number)
15606384476098624758…38609775145711861761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.121 Γ— 10⁹⁢(97-digit number)
31212768952197249517…77219550291423723521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.242 Γ— 10⁹⁢(97-digit number)
62425537904394499035…54439100582847447041
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 2812128

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 3eed165a0f1e6d54636821f44bd2e48831d8744df57af8f85bdf872981458bbd

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 #2,812,128 on Chainz β†—
Circulating Supply:57,937,688 XPMΒ·at block #6,836,675 Β· updates every 60s
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