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Home/Chain Registry/Block #2,727,405

Block #2,727,405

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/30/2018, 12:48:16 AM Β· Difficulty 11.6265 Β· 4,109,441 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7f5645c16c9920eece116bf5a4c5c16d0f8d968c9898d55d2761b381ad7831b9
View on Chainz β†—

Difficulty

11.626485

Transactions

1

Size

201 B

Version

2

Bits

0ba0614a

Nonce

167,132,309

Timestamp

6/30/2018, 12:48:16 AM

Confirmations

4,109,441

Merkle Root

f1589df9b231ea144bfb68d63d8e9cf9bbb7c9c2897b68499cbc09fefb6d72c2
Transactions (1)
Coinbasef1589df9b231ea…bc09fefb6d72c2
1 in β†’ 1 out7.3900 XPM110 B
AYaAusGz…1JW42eiH
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.

8.381 Γ— 10⁹⁡(96-digit number)
83817411754027088115…22303552629084056960
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
8.381 Γ— 10⁹⁡(96-digit number)
83817411754027088115…22303552629084056959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.676 Γ— 10⁹⁢(97-digit number)
16763482350805417623…44607105258168113919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.352 Γ— 10⁹⁢(97-digit number)
33526964701610835246…89214210516336227839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.705 Γ— 10⁹⁢(97-digit number)
67053929403221670492…78428421032672455679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.341 Γ— 10⁹⁷(98-digit number)
13410785880644334098…56856842065344911359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.682 Γ— 10⁹⁷(98-digit number)
26821571761288668196…13713684130689822719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.364 Γ— 10⁹⁷(98-digit number)
53643143522577336393…27427368261379645439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.072 Γ— 10⁹⁸(99-digit number)
10728628704515467278…54854736522759290879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.145 Γ— 10⁹⁸(99-digit number)
21457257409030934557…09709473045518581759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.291 Γ— 10⁹⁸(99-digit number)
42914514818061869115…19418946091037163519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.582 Γ— 10⁹⁸(99-digit number)
85829029636123738230…38837892182074327039
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 2727405

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 7f5645c16c9920eece116bf5a4c5c16d0f8d968c9898d55d2761b381ad7831b9

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 #2,727,405 on Chainz β†—
Circulating Supply:57,939,057 XPMΒ·at block #6,836,845 Β· updates every 60s
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