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Block #2,643,401

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 2:27:38 AM Β· Difficulty 11.6820 Β· 4,193,580 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
680ecd38a940360e3f44db987afeb64ff38117b3856a09bb39e830b71af844e1
View on Chainz β†—

Difficulty

11.682044

Transactions

1

Size

200 B

Version

2

Bits

0bae9a6f

Nonce

195,455,767

Timestamp

5/2/2018, 2:27:38 AM

Confirmations

4,193,580

Merkle Root

447d1825f910c647638e287f7f740c4063496a74b517feb72cde49753a8a70a3
Transactions (1)
Coinbase447d1825f910c6…de49753a8a70a3
1 in β†’ 1 out7.3200 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.

8.653 Γ— 10⁹³(94-digit number)
86533190482848863066…45422817594282229760
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
8.653 Γ— 10⁹³(94-digit number)
86533190482848863066…45422817594282229761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.730 Γ— 10⁹⁴(95-digit number)
17306638096569772613…90845635188564459521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.461 Γ— 10⁹⁴(95-digit number)
34613276193139545226…81691270377128919041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.922 Γ— 10⁹⁴(95-digit number)
69226552386279090453…63382540754257838081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.384 Γ— 10⁹⁡(96-digit number)
13845310477255818090…26765081508515676161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.769 Γ— 10⁹⁡(96-digit number)
27690620954511636181…53530163017031352321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.538 Γ— 10⁹⁡(96-digit number)
55381241909023272362…07060326034062704641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.107 Γ— 10⁹⁢(97-digit number)
11076248381804654472…14120652068125409281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.215 Γ— 10⁹⁢(97-digit number)
22152496763609308945…28241304136250818561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.430 Γ— 10⁹⁢(97-digit number)
44304993527218617890…56482608272501637121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.860 Γ— 10⁹⁢(97-digit number)
88609987054437235780…12965216545003274241
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 2643401

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 680ecd38a940360e3f44db987afeb64ff38117b3856a09bb39e830b71af844e1

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 #2,643,401 on Chainz β†—
Circulating Supply:57,940,147 XPMΒ·at block #6,836,980 Β· updates every 60s
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