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Home/Chain Registry/Block #2,643,154

Block #2,643,154

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 12:08:55 AM Β· Difficulty 11.6752 Β· 4,190,424 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
552932a742c4a0fe62cc75ed1e85bc4d1e364ac4b73742a7bccc1caf47caedc6
View on Chainz β†—

Difficulty

11.675165

Transactions

1

Size

200 B

Version

2

Bits

0bacd799

Nonce

469,023,799

Timestamp

5/2/2018, 12:08:55 AM

Confirmations

4,190,424

Merkle Root

e92a678a41558d39962e1b5e9a7d2c2faa800820e36743e0c4ecb288f001c676
Transactions (1)
Coinbasee92a678a41558d…ecb288f001c676
1 in β†’ 1 out7.3200 XPM110 B
AHQaQtQk…BDhbesSK
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.

1.151 Γ— 10⁹⁴(95-digit number)
11517316681081896088…87941069980188177920
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
1.151 Γ— 10⁹⁴(95-digit number)
11517316681081896088…87941069980188177919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.303 Γ— 10⁹⁴(95-digit number)
23034633362163792177…75882139960376355839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.606 Γ— 10⁹⁴(95-digit number)
46069266724327584354…51764279920752711679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.213 Γ— 10⁹⁴(95-digit number)
92138533448655168708…03528559841505423359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.842 Γ— 10⁹⁡(96-digit number)
18427706689731033741…07057119683010846719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.685 Γ— 10⁹⁡(96-digit number)
36855413379462067483…14114239366021693439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.371 Γ— 10⁹⁡(96-digit number)
73710826758924134966…28228478732043386879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.474 Γ— 10⁹⁢(97-digit number)
14742165351784826993…56456957464086773759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.948 Γ— 10⁹⁢(97-digit number)
29484330703569653986…12913914928173547519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.896 Γ— 10⁹⁢(97-digit number)
58968661407139307973…25827829856347095039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.179 Γ— 10⁹⁷(98-digit number)
11793732281427861594…51655659712694190079
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 2643154

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 552932a742c4a0fe62cc75ed1e85bc4d1e364ac4b73742a7bccc1caf47caedc6

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 #2,643,154 on Chainz β†—
Circulating Supply:57,912,828 XPMΒ·at block #6,833,577 Β· updates every 60s
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