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Home/Chain Registry/Block #2,764,074

Block #2,764,074

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/25/2018, 4:04:44 AM Β· Difficulty 11.6612 Β· 4,069,416 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b40477b282548b6c63629e1b3acd1c70ee50fc23df1a7ad487596c7dda089b01
View on Chainz β†—

Difficulty

11.661216

Transactions

1

Size

200 B

Version

2

Bits

0ba94571

Nonce

1,748,304,843

Timestamp

7/25/2018, 4:04:44 AM

Confirmations

4,069,416

Merkle Root

26b6b3229a0ec49281b08f6a3883e194272c6ab3932c3939a417640626d18d33
Transactions (1)
Coinbase26b6b3229a0ec4…17640626d18d33
1 in β†’ 1 out7.3400 XPM110 B
Ac3RUeT2…Lpf2zaVg
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.

2.252 Γ— 10⁹⁴(95-digit number)
22520282005410049809…23667008745738694480
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
2.252 Γ— 10⁹⁴(95-digit number)
22520282005410049809…23667008745738694481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.504 Γ— 10⁹⁴(95-digit number)
45040564010820099619…47334017491477388961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.008 Γ— 10⁹⁴(95-digit number)
90081128021640199238…94668034982954777921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.801 Γ— 10⁹⁡(96-digit number)
18016225604328039847…89336069965909555841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.603 Γ— 10⁹⁡(96-digit number)
36032451208656079695…78672139931819111681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.206 Γ— 10⁹⁡(96-digit number)
72064902417312159390…57344279863638223361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.441 Γ— 10⁹⁢(97-digit number)
14412980483462431878…14688559727276446721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.882 Γ— 10⁹⁢(97-digit number)
28825960966924863756…29377119454552893441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.765 Γ— 10⁹⁢(97-digit number)
57651921933849727512…58754238909105786881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.153 Γ— 10⁹⁷(98-digit number)
11530384386769945502…17508477818211573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.306 Γ— 10⁹⁷(98-digit number)
23060768773539891005…35016955636423147521
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 2764074

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 b40477b282548b6c63629e1b3acd1c70ee50fc23df1a7ad487596c7dda089b01

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 #2,764,074 on Chainz β†—
Circulating Supply:57,912,126 XPMΒ·at block #6,833,489 Β· updates every 60s
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