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Home/Chain Registry/Block #2,742,227

Block #2,742,227

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/10/2018, 6:51:04 AM Β· Difficulty 11.6314 Β· 4,103,423 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c7890380208f5020486b28f64e2f65fa4a5418c03ad307b824dd792565254018
View on Chainz β†—

Difficulty

11.631388

Transactions

1

Size

199 B

Version

2

Bits

0ba1a2a2

Nonce

282,676,608

Timestamp

7/10/2018, 6:51:04 AM

Confirmations

4,103,423

Merkle Root

8ee3a064d12b8774fb6cf0572dc911e35ecef340e3b2eef5a2f927bf6279feb1
Transactions (1)
Coinbase8ee3a064d12b87…f927bf6279feb1
1 in β†’ 1 out7.3800 XPM109 B
AZtxQr2F…7grUWrUz
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.

1.476 Γ— 10⁹⁡(96-digit number)
14760249464538548043…64445802207557550720
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
1.476 Γ— 10⁹⁡(96-digit number)
14760249464538548043…64445802207557550719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.952 Γ— 10⁹⁡(96-digit number)
29520498929077096086…28891604415115101439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.904 Γ— 10⁹⁡(96-digit number)
59040997858154192173…57783208830230202879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁢(97-digit number)
11808199571630838434…15566417660460405759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.361 Γ— 10⁹⁢(97-digit number)
23616399143261676869…31132835320920811519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.723 Γ— 10⁹⁢(97-digit number)
47232798286523353739…62265670641841623039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.446 Γ— 10⁹⁢(97-digit number)
94465596573046707478…24531341283683246079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.889 Γ— 10⁹⁷(98-digit number)
18893119314609341495…49062682567366492159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.778 Γ— 10⁹⁷(98-digit number)
37786238629218682991…98125365134732984319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.557 Γ— 10⁹⁷(98-digit number)
75572477258437365982…96250730269465968639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.511 Γ— 10⁹⁸(99-digit number)
15114495451687473196…92501460538931937279
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 2742227

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 c7890380208f5020486b28f64e2f65fa4a5418c03ad307b824dd792565254018

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 #2,742,227 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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