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Home/Chain Registry/Block #2,643,292

Block #2,643,292

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 1:31:53 AM Β· Difficulty 11.6787 Β· 4,196,825 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2211f292e10116e04a04c0b3c92655e4287a50fc3a9bf62d0015a43acbadf339
View on Chainz β†—

Difficulty

11.678717

Transactions

1

Size

201 B

Version

2

Bits

0badc062

Nonce

667,761,491

Timestamp

5/2/2018, 1:31:53 AM

Confirmations

4,196,825

Merkle Root

f7a699c9790826a68322e285fc2f0d1918debbc541c177dcaa8ce6dd9c00977f
Transactions (1)
Coinbasef7a699c9790826…8ce6dd9c00977f
1 in β†’ 1 out7.3200 XPM110 B
AUS1ZASa…o7fYyUpE
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.

2.124 Γ— 10⁹⁢(97-digit number)
21241179357503800647…37325248368558080000
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
2.124 Γ— 10⁹⁢(97-digit number)
21241179357503800647…37325248368558079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.248 Γ— 10⁹⁢(97-digit number)
42482358715007601295…74650496737116159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.496 Γ— 10⁹⁢(97-digit number)
84964717430015202591…49300993474232319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.699 Γ— 10⁹⁷(98-digit number)
16992943486003040518…98601986948464639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.398 Γ— 10⁹⁷(98-digit number)
33985886972006081036…97203973896929279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.797 Γ— 10⁹⁷(98-digit number)
67971773944012162073…94407947793858559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.359 Γ— 10⁹⁸(99-digit number)
13594354788802432414…88815895587717119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.718 Γ— 10⁹⁸(99-digit number)
27188709577604864829…77631791175434239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.437 Γ— 10⁹⁸(99-digit number)
54377419155209729658…55263582350868479999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.087 Γ— 10⁹⁹(100-digit number)
10875483831041945931…10527164701736959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.175 Γ— 10⁹⁹(100-digit number)
21750967662083891863…21054329403473919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
4.350 Γ— 10⁹⁹(100-digit number)
43501935324167783727…42108658806947839999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2643292

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 2211f292e10116e04a04c0b3c92655e4287a50fc3a9bf62d0015a43acbadf339

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 #2,643,292 on Chainz β†—
Circulating Supply:57,965,248 XPMΒ·at block #6,840,116 Β· updates every 60s
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