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Block #2,645,682

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 12:35:08 AM Β· Difficulty 11.7370 Β· 4,195,878 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
38bf32efaf78e5688f6ef741cde7361c3248417abc87add84295b1dbce4c8e6a
View on Chainz β†—

Difficulty

11.736951

Transactions

1

Size

200 B

Version

2

Bits

0bbca8cb

Nonce

1,458,808,167

Timestamp

5/3/2018, 12:35:08 AM

Confirmations

4,195,878

Merkle Root

67c22e0f7d9b4c9a3d9424b0ea735f0a9f647fc43896c2600cd59613c3a552fd
Transactions (1)
Coinbase67c22e0f7d9b4c…d59613c3a552fd
1 in β†’ 1 out7.2500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.082 Γ— 10⁹⁡(96-digit number)
10820822758224927095…33587546968103517400
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
1.082 Γ— 10⁹⁡(96-digit number)
10820822758224927095…33587546968103517401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.164 Γ— 10⁹⁡(96-digit number)
21641645516449854191…67175093936207034801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.328 Γ— 10⁹⁡(96-digit number)
43283291032899708382…34350187872414069601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.656 Γ— 10⁹⁡(96-digit number)
86566582065799416764…68700375744828139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.731 Γ— 10⁹⁢(97-digit number)
17313316413159883352…37400751489656278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.462 Γ— 10⁹⁢(97-digit number)
34626632826319766705…74801502979312556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.925 Γ— 10⁹⁢(97-digit number)
69253265652639533411…49603005958625113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.385 Γ— 10⁹⁷(98-digit number)
13850653130527906682…99206011917250227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.770 Γ— 10⁹⁷(98-digit number)
27701306261055813364…98412023834500454401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.540 Γ— 10⁹⁷(98-digit number)
55402612522111626729…96824047669000908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.108 Γ— 10⁹⁸(99-digit number)
11080522504422325345…93648095338001817601
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 2645682

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 38bf32efaf78e5688f6ef741cde7361c3248417abc87add84295b1dbce4c8e6a

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 #2,645,682 on Chainz β†—
Circulating Supply:57,976,863 XPMΒ·at block #6,841,559 Β· updates every 60s
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