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Home/Chain Registry/Block #2,110,107

Block #2,110,107

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/10/2017, 1:52:17 PM Β· Difficulty 10.9020 Β· 4,732,647 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c8702bf26b8931fb6188f0f37a7dc8d4b5aacb3ad09c0b100505760473c0cde
View on Chainz β†—

Difficulty

10.901964

Transactions

1

Size

200 B

Version

2

Bits

0ae6e720

Nonce

1,367,479,978

Timestamp

5/10/2017, 1:52:17 PM

Confirmations

4,732,647

Merkle Root

04952ab6da6ce2da02905177080e74c56dc74194cb4f2cb12662c21fb355652a
Transactions (1)
Coinbase04952ab6da6ce2…62c21fb355652a
1 in β†’ 1 out8.4000 XPM110 B
AZp3HsBP…qqkPNkUb
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.

3.392 Γ— 10⁹³(94-digit number)
33922640561951020434…00580376257010641500
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
3.392 Γ— 10⁹³(94-digit number)
33922640561951020434…00580376257010641501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.784 Γ— 10⁹³(94-digit number)
67845281123902040868…01160752514021283001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.356 Γ— 10⁹⁴(95-digit number)
13569056224780408173…02321505028042566001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.713 Γ— 10⁹⁴(95-digit number)
27138112449560816347…04643010056085132001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.427 Γ— 10⁹⁴(95-digit number)
54276224899121632694…09286020112170264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.085 Γ— 10⁹⁡(96-digit number)
10855244979824326538…18572040224340528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.171 Γ— 10⁹⁡(96-digit number)
21710489959648653077…37144080448681056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.342 Γ— 10⁹⁡(96-digit number)
43420979919297306155…74288160897362112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.684 Γ— 10⁹⁡(96-digit number)
86841959838594612311…48576321794724224001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.736 Γ— 10⁹⁢(97-digit number)
17368391967718922462…97152643589448448001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.473 Γ— 10⁹⁢(97-digit number)
34736783935437844924…94305287178896896001
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 2110107

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 6c8702bf26b8931fb6188f0f37a7dc8d4b5aacb3ad09c0b100505760473c0cde

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 #2,110,107 on Chainz β†—
Circulating Supply:57,986,370 XPMΒ·at block #6,842,753 Β· updates every 60s
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