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Home/Chain Registry/Block #2,646,067

Block #2,646,067

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 4:41:07 AM Β· Difficulty 11.7441 Β· 4,191,533 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8c92d6e83fb562fe4d031d472a5865a27a248abe558497eceacfa05b68971db3
View on Chainz β†—

Difficulty

11.744102

Transactions

1

Size

200 B

Version

2

Bits

0bbe7d7c

Nonce

260,796,965

Timestamp

5/3/2018, 4:41:07 AM

Confirmations

4,191,533

Merkle Root

6733a3dee8273d757aa30debf0f7e16adf472eb369fcc803984db0f6421e5934
Transactions (1)
Coinbase6733a3dee8273d…4db0f6421e5934
1 in β†’ 1 out7.2400 XPM110 B
ARnJkJtY…abwLqSKR
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.

4.456 Γ— 10⁹⁴(95-digit number)
44560481436765520234…39456033840335138700
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
4.456 Γ— 10⁹⁴(95-digit number)
44560481436765520234…39456033840335138701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.912 Γ— 10⁹⁴(95-digit number)
89120962873531040468…78912067680670277401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.782 Γ— 10⁹⁡(96-digit number)
17824192574706208093…57824135361340554801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.564 Γ— 10⁹⁡(96-digit number)
35648385149412416187…15648270722681109601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.129 Γ— 10⁹⁡(96-digit number)
71296770298824832375…31296541445362219201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.425 Γ— 10⁹⁢(97-digit number)
14259354059764966475…62593082890724438401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.851 Γ— 10⁹⁢(97-digit number)
28518708119529932950…25186165781448876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.703 Γ— 10⁹⁢(97-digit number)
57037416239059865900…50372331562897753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.140 Γ— 10⁹⁷(98-digit number)
11407483247811973180…00744663125795507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.281 Γ— 10⁹⁷(98-digit number)
22814966495623946360…01489326251591014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.562 Γ— 10⁹⁷(98-digit number)
45629932991247892720…02978652503182028801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
9.125 Γ— 10⁹⁷(98-digit number)
91259865982495785440…05957305006364057601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2646067

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 8c92d6e83fb562fe4d031d472a5865a27a248abe558497eceacfa05b68971db3

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 #2,646,067 on Chainz β†—
Circulating Supply:57,945,123 XPMΒ·at block #6,837,599 Β· updates every 60s
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