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Home/Chain Registry/Block #2,668,806

Block #2,668,806

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/19/2018, 7:23:51 PM Β· Difficulty 11.6773 Β· 4,163,117 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5cf16d589be6ab745662e75a1d843c09fcf78e0b937824b651d500a9110a505f
View on Chainz β†—

Difficulty

11.677299

Transactions

1

Size

201 B

Version

2

Bits

0bad6379

Nonce

713,349,101

Timestamp

5/19/2018, 7:23:51 PM

Confirmations

4,163,117

Merkle Root

9a31082ecf8aebc312e544b819025066a6d6eb84173c20c2150f7416f3090007
Transactions (1)
Coinbase9a31082ecf8aeb…0f7416f3090007
1 in β†’ 1 out7.3200 XPM110 B
AdSwjara…NVE7efrQ
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.

1.257 Γ— 10⁹⁢(97-digit number)
12572484503076537455…11948345982840371200
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
1.257 Γ— 10⁹⁢(97-digit number)
12572484503076537455…11948345982840371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.514 Γ— 10⁹⁢(97-digit number)
25144969006153074910…23896691965680742399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.028 Γ— 10⁹⁢(97-digit number)
50289938012306149821…47793383931361484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.005 Γ— 10⁹⁷(98-digit number)
10057987602461229964…95586767862722969599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.011 Γ— 10⁹⁷(98-digit number)
20115975204922459928…91173535725445939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.023 Γ— 10⁹⁷(98-digit number)
40231950409844919856…82347071450891878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.046 Γ— 10⁹⁷(98-digit number)
80463900819689839713…64694142901783756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.609 Γ— 10⁹⁸(99-digit number)
16092780163937967942…29388285803567513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.218 Γ— 10⁹⁸(99-digit number)
32185560327875935885…58776571607135027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.437 Γ— 10⁹⁸(99-digit number)
64371120655751871770…17553143214270054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.287 Γ— 10⁹⁹(100-digit number)
12874224131150374354…35106286428540108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.574 Γ— 10⁹⁹(100-digit number)
25748448262300748708…70212572857080217599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2668806

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 5cf16d589be6ab745662e75a1d843c09fcf78e0b937824b651d500a9110a505f

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 #2,668,806 on Chainz β†—
Circulating Supply:57,899,510 XPMΒ·at block #6,831,922 Β· updates every 60s
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