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Home/Chain Registry/Block #2,640,084

Block #2,640,084

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 9:14:36 PM Β· Difficulty 11.5663 Β· 4,190,942 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
93f8f67b894324a87df5ee88c2a65e432014bb1edcf7138ff8c4fc1808b9c50a
View on Chainz β†—

Difficulty

11.566294

Transactions

1

Size

200 B

Version

2

Bits

0b90f8a4

Nonce

579,008,684

Timestamp

4/30/2018, 9:14:36 PM

Confirmations

4,190,942

Merkle Root

6e4e768178857a492944a1875d94bba1c36aa566d8959013678951a2d0567549
Transactions (1)
Coinbase6e4e768178857a…8951a2d0567549
1 in β†’ 1 out7.4600 XPM110 B
AZUhpE1g…XUpFqdLj
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.

1.276 Γ— 10⁹⁡(96-digit number)
12763611345495737511…38754645529674241920
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
1.276 Γ— 10⁹⁡(96-digit number)
12763611345495737511…38754645529674241921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.552 Γ— 10⁹⁡(96-digit number)
25527222690991475023…77509291059348483841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.105 Γ— 10⁹⁡(96-digit number)
51054445381982950047…55018582118696967681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.021 Γ— 10⁹⁢(97-digit number)
10210889076396590009…10037164237393935361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.042 Γ— 10⁹⁢(97-digit number)
20421778152793180018…20074328474787870721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.084 Γ— 10⁹⁢(97-digit number)
40843556305586360037…40148656949575741441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.168 Γ— 10⁹⁢(97-digit number)
81687112611172720075…80297313899151482881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.633 Γ— 10⁹⁷(98-digit number)
16337422522234544015…60594627798302965761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.267 Γ— 10⁹⁷(98-digit number)
32674845044469088030…21189255596605931521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.534 Γ— 10⁹⁷(98-digit number)
65349690088938176060…42378511193211863041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.306 Γ— 10⁹⁸(99-digit number)
13069938017787635212…84757022386423726081
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 2640084

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 93f8f67b894324a87df5ee88c2a65e432014bb1edcf7138ff8c4fc1808b9c50a

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 #2,640,084 on Chainz β†—
Circulating Supply:57,892,342 XPMΒ·at block #6,831,025 Β· updates every 60s
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