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Home/Chain Registry/Block #2,645,583

Block #2,645,583

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 11:34:46 PM Β· Difficulty 11.7349 Β· 4,196,504 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e7fab9cd4abc0f92324241260061e1f3ddc68d0ce5a01eaac3022efd2e290e43
View on Chainz β†—

Difficulty

11.734905

Transactions

1

Size

200 B

Version

2

Bits

0bbc22b5

Nonce

1,407,701,557

Timestamp

5/2/2018, 11:34:46 PM

Confirmations

4,196,504

Merkle Root

deee625fd50c65a052167f72998c59689ed647de2a41d0d934b40e4611c4f3d3
Transactions (1)
Coinbasedeee625fd50c65…b40e4611c4f3d3
1 in β†’ 1 out7.2500 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.

1.875 Γ— 10⁹⁡(96-digit number)
18754726150463516761…86106820961948505600
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
1.875 Γ— 10⁹⁡(96-digit number)
18754726150463516761…86106820961948505601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.750 Γ— 10⁹⁡(96-digit number)
37509452300927033522…72213641923897011201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.501 Γ— 10⁹⁡(96-digit number)
75018904601854067045…44427283847794022401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.500 Γ— 10⁹⁢(97-digit number)
15003780920370813409…88854567695588044801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.000 Γ— 10⁹⁢(97-digit number)
30007561840741626818…77709135391176089601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.001 Γ— 10⁹⁢(97-digit number)
60015123681483253636…55418270782352179201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.200 Γ— 10⁹⁷(98-digit number)
12003024736296650727…10836541564704358401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.400 Γ— 10⁹⁷(98-digit number)
24006049472593301454…21673083129408716801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.801 Γ— 10⁹⁷(98-digit number)
48012098945186602909…43346166258817433601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.602 Γ— 10⁹⁷(98-digit number)
96024197890373205818…86692332517634867201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.920 Γ— 10⁹⁸(99-digit number)
19204839578074641163…73384665035269734401
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 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
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 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 2645583

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 e7fab9cd4abc0f92324241260061e1f3ddc68d0ce5a01eaac3022efd2e290e43

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 #2,645,583 on Chainz β†—
Circulating Supply:57,981,081 XPMΒ·at block #6,842,086 Β· updates every 60s
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