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Home/Chain Registry/Block #2,640,286

Block #2,640,286

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 10:54:23 PM Β· Difficulty 11.5750 Β· 4,190,733 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
41da7428cde24a3d06a1ce7718fa5b4df1c41aa65ed01a863db6d898521b9950
View on Chainz β†—

Difficulty

11.574969

Transactions

1

Size

201 B

Version

2

Bits

0b933131

Nonce

399,815,281

Timestamp

4/30/2018, 10:54:23 PM

Confirmations

4,190,733

Merkle Root

fc8e4d63559706c70a0ac71b798e9e0a585fe4533b16bfb6a13d1b14af94d517
Transactions (1)
Coinbasefc8e4d63559706…3d1b14af94d517
1 in β†’ 1 out7.4500 XPM110 B
AMPuAfYS…e2hDpYvB
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.

7.994 Γ— 10⁹⁡(96-digit number)
79947101578071065576…84346757905780257280
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
7.994 Γ— 10⁹⁡(96-digit number)
79947101578071065576…84346757905780257281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.598 Γ— 10⁹⁢(97-digit number)
15989420315614213115…68693515811560514561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.197 Γ— 10⁹⁢(97-digit number)
31978840631228426230…37387031623121029121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.395 Γ— 10⁹⁢(97-digit number)
63957681262456852461…74774063246242058241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.279 Γ— 10⁹⁷(98-digit number)
12791536252491370492…49548126492484116481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.558 Γ— 10⁹⁷(98-digit number)
25583072504982740984…99096252984968232961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.116 Γ— 10⁹⁷(98-digit number)
51166145009965481968…98192505969936465921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.023 Γ— 10⁹⁸(99-digit number)
10233229001993096393…96385011939872931841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.046 Γ— 10⁹⁸(99-digit number)
20466458003986192787…92770023879745863681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.093 Γ— 10⁹⁸(99-digit number)
40932916007972385575…85540047759491727361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.186 Γ— 10⁹⁸(99-digit number)
81865832015944771150…71080095518983454721
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 2640286

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 41da7428cde24a3d06a1ce7718fa5b4df1c41aa65ed01a863db6d898521b9950

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 #2,640,286 on Chainz β†—
Circulating Supply:57,892,293 XPMΒ·at block #6,831,018 Β· updates every 60s
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