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Home/Chain Registry/Block #2,244,100

Block #2,244,100

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2017, 4:23:42 PM Β· Difficulty 10.9470 Β· 4,592,879 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bf4fb2ba952358558a189c574ac36c9f40c3a7794ea1507ec8d1258031c0e4b4
View on Chainz β†—

Difficulty

10.947014

Transactions

1

Size

200 B

Version

2

Bits

0af26f7d

Nonce

790,668,952

Timestamp

8/9/2017, 4:23:42 PM

Confirmations

4,592,879

Merkle Root

2f2b575e1777cfd107cdd1bbbb9b2ad87368eff0d5288c46cf720b1182093110
Transactions (1)
Coinbase2f2b575e1777cf…720b1182093110
1 in β†’ 1 out8.3300 XPM110 B
ASBUZCw8…8y1DyQvi
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.

4.711 Γ— 10⁹⁡(96-digit number)
47113212205971718331…88888220395173376000
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
4.711 Γ— 10⁹⁡(96-digit number)
47113212205971718331…88888220395173376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.422 Γ— 10⁹⁡(96-digit number)
94226424411943436663…77776440790346752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.884 Γ— 10⁹⁢(97-digit number)
18845284882388687332…55552881580693504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.769 Γ— 10⁹⁢(97-digit number)
37690569764777374665…11105763161387008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.538 Γ— 10⁹⁢(97-digit number)
75381139529554749330…22211526322774016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.507 Γ— 10⁹⁷(98-digit number)
15076227905910949866…44423052645548032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.015 Γ— 10⁹⁷(98-digit number)
30152455811821899732…88846105291096064001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.030 Γ— 10⁹⁷(98-digit number)
60304911623643799464…77692210582192128001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.206 Γ— 10⁹⁸(99-digit number)
12060982324728759892…55384421164384256001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.412 Γ— 10⁹⁸(99-digit number)
24121964649457519785…10768842328768512001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2244100

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 bf4fb2ba952358558a189c574ac36c9f40c3a7794ea1507ec8d1258031c0e4b4

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 #2,244,100 on Chainz β†—
Circulating Supply:57,940,131 XPMΒ·at block #6,836,978 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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