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Home/Chain Registry/Block #2,843,669

Block #2,843,669

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2018, 5:14:09 PM Β· Difficulty 11.7270 Β· 4,000,244 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
74a2685fb21d4f38b6f536c6c81238c596b08cc0991b0313a58a07eb61f21d5f
View on Chainz β†—

Difficulty

11.727015

Transactions

1

Size

200 B

Version

2

Bits

0bba1dae

Nonce

1,130,904,775

Timestamp

9/17/2018, 5:14:09 PM

Confirmations

4,000,244

Merkle Root

0fdc5a8d9df1b4405320f87a200844e62d719a2548cd88f78d4f826edef8d80b
Transactions (1)
Coinbase0fdc5a8d9df1b4…4f826edef8d80b
1 in β†’ 1 out7.2600 XPM110 B
AatBBXmH…BCwBjnQG
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.

2.549 Γ— 10⁹⁴(95-digit number)
25490332521402148231…65572474952563055040
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.549 Γ— 10⁹⁴(95-digit number)
25490332521402148231…65572474952563055039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.098 Γ— 10⁹⁴(95-digit number)
50980665042804296462…31144949905126110079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.019 Γ— 10⁹⁡(96-digit number)
10196133008560859292…62289899810252220159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.039 Γ— 10⁹⁡(96-digit number)
20392266017121718584…24579799620504440319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.078 Γ— 10⁹⁡(96-digit number)
40784532034243437169…49159599241008880639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.156 Γ— 10⁹⁡(96-digit number)
81569064068486874339…98319198482017761279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.631 Γ— 10⁹⁢(97-digit number)
16313812813697374867…96638396964035522559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.262 Γ— 10⁹⁢(97-digit number)
32627625627394749735…93276793928071045119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.525 Γ— 10⁹⁢(97-digit number)
65255251254789499471…86553587856142090239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁷(98-digit number)
13051050250957899894…73107175712284180479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.610 Γ— 10⁹⁷(98-digit number)
26102100501915799788…46214351424568360959
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2843669

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 74a2685fb21d4f38b6f536c6c81238c596b08cc0991b0313a58a07eb61f21d5f

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 #2,843,669 on Chainz β†—
Circulating Supply:57,995,675 XPMΒ·at block #6,843,912 Β· updates every 60s
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