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Home/Chain Registry/Block #2,809,224

Block #2,809,224

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/25/2018, 11:38:08 AM Β· Difficulty 11.6665 Β· 4,032,825 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e11257faaa5ed2cce543d29d9bffeecb010966f2b0c2a59f91883e6c6a5e6d54
View on Chainz β†—

Difficulty

11.666506

Transactions

1

Size

200 B

Version

2

Bits

0baaa023

Nonce

1,346,814,652

Timestamp

8/25/2018, 11:38:08 AM

Confirmations

4,032,825

Merkle Root

1b731de20bdb8e9cec3b30d26a339f23e6a1bbaf854a1cfcb3efa15595baba0f
Transactions (1)
Coinbase1b731de20bdb8e…efa15595baba0f
1 in β†’ 1 out7.3300 XPM110 B
AduUDLiu…86zx6F2J
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.

7.446 Γ— 10⁹⁡(96-digit number)
74467722487036596347…14090025378606011520
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
7.446 Γ— 10⁹⁡(96-digit number)
74467722487036596347…14090025378606011521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.489 Γ— 10⁹⁢(97-digit number)
14893544497407319269…28180050757212023041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.978 Γ— 10⁹⁢(97-digit number)
29787088994814638538…56360101514424046081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.957 Γ— 10⁹⁢(97-digit number)
59574177989629277077…12720203028848092161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.191 Γ— 10⁹⁷(98-digit number)
11914835597925855415…25440406057696184321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.382 Γ— 10⁹⁷(98-digit number)
23829671195851710831…50880812115392368641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.765 Γ— 10⁹⁷(98-digit number)
47659342391703421662…01761624230784737281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.531 Γ— 10⁹⁷(98-digit number)
95318684783406843324…03523248461569474561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.906 Γ— 10⁹⁸(99-digit number)
19063736956681368664…07046496923138949121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.812 Γ— 10⁹⁸(99-digit number)
38127473913362737329…14092993846277898241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.625 Γ— 10⁹⁸(99-digit number)
76254947826725474659…28185987692555796481
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 2809224

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 e11257faaa5ed2cce543d29d9bffeecb010966f2b0c2a59f91883e6c6a5e6d54

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 #2,809,224 on Chainz β†—
Circulating Supply:57,980,773 XPMΒ·at block #6,842,048 Β· updates every 60s
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