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Block #2,646,532

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2018, 10:12:54 AM Β· Difficulty 11.7508 Β· 4,187,192 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8c6927aaca5c250a0fe4b46f906847c34c7da5fadfdd5b7c7d0e3c61a5790f01
View on Chainz β†—

Difficulty

11.750785

Transactions

1

Size

200 B

Version

2

Bits

0bc03379

Nonce

122,370,600

Timestamp

5/3/2018, 10:12:54 AM

Confirmations

4,187,192

Merkle Root

bd9f9a6d189fa42076c5f16409d70d203fc284aa60150152111c19bb9c914b65
Transactions (1)
Coinbasebd9f9a6d189fa4…1c19bb9c914b65
1 in β†’ 1 out7.2300 XPM110 B
ANxRjg8m…LttMhq7y
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.

1.041 Γ— 10⁹⁡(96-digit number)
10416279416278837392…92294963935796014080
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
1.041 Γ— 10⁹⁡(96-digit number)
10416279416278837392…92294963935796014079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.083 Γ— 10⁹⁡(96-digit number)
20832558832557674784…84589927871592028159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.166 Γ— 10⁹⁡(96-digit number)
41665117665115349568…69179855743184056319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.333 Γ— 10⁹⁡(96-digit number)
83330235330230699137…38359711486368112639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.666 Γ— 10⁹⁢(97-digit number)
16666047066046139827…76719422972736225279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.333 Γ— 10⁹⁢(97-digit number)
33332094132092279655…53438845945472450559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.666 Γ— 10⁹⁢(97-digit number)
66664188264184559310…06877691890944901119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.333 Γ— 10⁹⁷(98-digit number)
13332837652836911862…13755383781889802239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.666 Γ— 10⁹⁷(98-digit number)
26665675305673823724…27510767563779604479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.333 Γ— 10⁹⁷(98-digit number)
53331350611347647448…55021535127559208959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.066 Γ— 10⁹⁸(99-digit number)
10666270122269529489…10043070255118417919
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 2646532

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 8c6927aaca5c250a0fe4b46f906847c34c7da5fadfdd5b7c7d0e3c61a5790f01

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 #2,646,532 on Chainz β†—
Circulating Supply:57,914,014 XPMΒ·at block #6,833,723 Β· updates every 60s
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