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Block #2,640,285

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 10:54:10 PM Β· Difficulty 11.5749 Β· 4,191,055 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e60c947d42bbfdeb46de8e99d8e262b5cfcc2b932e13c93c0aa4a9fd27fe85f7
View on Chainz β†—

Difficulty

11.574938

Transactions

1

Size

199 B

Version

2

Bits

0b932f2a

Nonce

287,021,640

Timestamp

4/30/2018, 10:54:10 PM

Confirmations

4,191,055

Merkle Root

8f03c9a61f0d4376b9f9e78b6233a96dbf7891e86078fecd487a0b721f2ec067
Transactions (1)
Coinbase8f03c9a61f0d43…7a0b721f2ec067
1 in β†’ 1 out7.4500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

5.774 Γ— 10⁹¹(92-digit number)
57742436517299418211…36174974124315144560
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
5.774 Γ— 10⁹¹(92-digit number)
57742436517299418211…36174974124315144559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.154 Γ— 10⁹²(93-digit number)
11548487303459883642…72349948248630289119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.309 Γ— 10⁹²(93-digit number)
23096974606919767284…44699896497260578239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.619 Γ— 10⁹²(93-digit number)
46193949213839534568…89399792994521156479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.238 Γ— 10⁹²(93-digit number)
92387898427679069137…78799585989042312959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.847 Γ— 10⁹³(94-digit number)
18477579685535813827…57599171978084625919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.695 Γ— 10⁹³(94-digit number)
36955159371071627655…15198343956169251839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.391 Γ— 10⁹³(94-digit number)
73910318742143255310…30396687912338503679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.478 Γ— 10⁹⁴(95-digit number)
14782063748428651062…60793375824677007359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.956 Γ— 10⁹⁴(95-digit number)
29564127496857302124…21586751649354014719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.912 Γ— 10⁹⁴(95-digit number)
59128254993714604248…43173503298708029439
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 2640285

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 e60c947d42bbfdeb46de8e99d8e262b5cfcc2b932e13c93c0aa4a9fd27fe85f7

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 #2,640,285 on Chainz β†—
Circulating Supply:57,894,873 XPMΒ·at block #6,831,339 Β· updates every 60s
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