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Home/Chain Registry/Block #2,762,020

Block #2,762,020

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/23/2018, 7:31:06 PM Β· Difficulty 11.6543 Β· 4,071,289 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d72290e0c72983f79041cb89bb6e034a0a4cd217b4d924f01533a4961111a803
View on Chainz β†—

Difficulty

11.654307

Transactions

2

Size

1.14 KB

Version

2

Bits

0ba780ae

Nonce

1,557,612,902

Timestamp

7/23/2018, 7:31:06 PM

Confirmations

4,071,289

Merkle Root

43974bfac5686511ad271d213025384f1f000186edcbe50d38da3b84563b5556
Transactions (2)
Coinbase64c7fd1ab03aa9…f432b2418a262b
1 in β†’ 1 out7.3600 XPM110 B
AVe5ndMK…1u5QgQvM
9c887db8b51d76…9caedb0bf0e833
6 in β†’ 2 out177.6791 XPM964 B
ATJBxB2s…Kq5sntJtAbiZw7N1…HPacQJfk
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.

1.001 Γ— 10⁹⁡(96-digit number)
10015280868760977199…28465729545626201740
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
1.001 Γ— 10⁹⁡(96-digit number)
10015280868760977199…28465729545626201741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.003 Γ— 10⁹⁡(96-digit number)
20030561737521954398…56931459091252403481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.006 Γ— 10⁹⁡(96-digit number)
40061123475043908796…13862918182504806961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.012 Γ— 10⁹⁡(96-digit number)
80122246950087817593…27725836365009613921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.602 Γ— 10⁹⁢(97-digit number)
16024449390017563518…55451672730019227841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.204 Γ— 10⁹⁢(97-digit number)
32048898780035127037…10903345460038455681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.409 Γ— 10⁹⁢(97-digit number)
64097797560070254074…21806690920076911361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.281 Γ— 10⁹⁷(98-digit number)
12819559512014050814…43613381840153822721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.563 Γ— 10⁹⁷(98-digit number)
25639119024028101629…87226763680307645441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.127 Γ— 10⁹⁷(98-digit number)
51278238048056203259…74453527360615290881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.025 Γ— 10⁹⁸(99-digit number)
10255647609611240651…48907054721230581761
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 2762020

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 d72290e0c72983f79041cb89bb6e034a0a4cd217b4d924f01533a4961111a803

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 #2,762,020 on Chainz β†—
Circulating Supply:57,910,662 XPMΒ·at block #6,833,308 Β· updates every 60s
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