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Home/Chain Registry/Block #3,364,735

Block #3,364,735

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/22/2019, 7:55:38 AM Β· Difficulty 10.9954 Β· 3,462,179 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a88da11f365aa5699bb6fa409d2557aab571d669089ebda93e5b23f60ba995af
View on Chainz β†—

Difficulty

10.995448

Transactions

1

Size

200 B

Version

2

Bits

0afed5a6

Nonce

442,897,621

Timestamp

9/22/2019, 7:55:38 AM

Confirmations

3,462,179

Merkle Root

cc7fb754a37f5d06103d024d1817fd2490d24d8727304fa97a7dd18f79cf3015
Transactions (1)
Coinbasecc7fb754a37f5d…7dd18f79cf3015
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

2.239 Γ— 10⁹⁴(95-digit number)
22399019054816246452…07730697171537697440
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
2.239 Γ— 10⁹⁴(95-digit number)
22399019054816246452…07730697171537697439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.479 Γ— 10⁹⁴(95-digit number)
44798038109632492905…15461394343075394879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.959 Γ— 10⁹⁴(95-digit number)
89596076219264985810…30922788686150789759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.791 Γ— 10⁹⁡(96-digit number)
17919215243852997162…61845577372301579519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.583 Γ— 10⁹⁡(96-digit number)
35838430487705994324…23691154744603159039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.167 Γ— 10⁹⁡(96-digit number)
71676860975411988648…47382309489206318079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.433 Γ— 10⁹⁢(97-digit number)
14335372195082397729…94764618978412636159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.867 Γ— 10⁹⁢(97-digit number)
28670744390164795459…89529237956825272319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.734 Γ— 10⁹⁢(97-digit number)
57341488780329590918…79058475913650544639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.146 Γ— 10⁹⁷(98-digit number)
11468297756065918183…58116951827301089279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.293 Γ— 10⁹⁷(98-digit number)
22936595512131836367…16233903654602178559
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 3364735

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 a88da11f365aa5699bb6fa409d2557aab571d669089ebda93e5b23f60ba995af

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 #3,364,735 on Chainz β†—
Circulating Supply:57,859,481 XPMΒ·at block #6,826,913 Β· updates every 60s
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