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Home/Chain Registry/Block #3,335,927

Block #3,335,927

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/1/2019, 5:45:51 AM Β· Difficulty 11.0010 Β· 3,507,487 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ed337a4ce9b4baf4e79ef703b0239acdaca993a087bc268f391d88d1c3cb542a
View on Chainz β†—

Difficulty

11.000968

Transactions

1

Size

201 B

Version

2

Bits

0b003f77

Nonce

616,762,011

Timestamp

9/1/2019, 5:45:51 AM

Confirmations

3,507,487

Merkle Root

46d943761237325500e91c4f5269658bb81f9c3357908ca718d9992386614b18
Transactions (1)
Coinbase46d94376123732…d9992386614b18
1 in β†’ 1 out8.2500 XPM110 B
AXfJqzUb…HXeXmjMz
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.

1.792 Γ— 10⁹⁢(97-digit number)
17922510232630378139…48172465566453721920
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
1.792 Γ— 10⁹⁢(97-digit number)
17922510232630378139…48172465566453721921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.584 Γ— 10⁹⁢(97-digit number)
35845020465260756278…96344931132907443841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.169 Γ— 10⁹⁢(97-digit number)
71690040930521512557…92689862265814887681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.433 Γ— 10⁹⁷(98-digit number)
14338008186104302511…85379724531629775361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.867 Γ— 10⁹⁷(98-digit number)
28676016372208605022…70759449063259550721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.735 Γ— 10⁹⁷(98-digit number)
57352032744417210045…41518898126519101441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.147 Γ— 10⁹⁸(99-digit number)
11470406548883442009…83037796253038202881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.294 Γ— 10⁹⁸(99-digit number)
22940813097766884018…66075592506076405761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.588 Γ— 10⁹⁸(99-digit number)
45881626195533768036…32151185012152811521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.176 Γ— 10⁹⁸(99-digit number)
91763252391067536073…64302370024305623041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.835 Γ— 10⁹⁹(100-digit number)
18352650478213507214…28604740048611246081
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 3335927

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 ed337a4ce9b4baf4e79ef703b0239acdaca993a087bc268f391d88d1c3cb542a

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 #3,335,927 on Chainz β†—
Circulating Supply:57,991,679 XPMΒ·at block #6,843,413 Β· updates every 60s
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