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Home/Chain Registry/Block #2,640,142

Block #2,640,142

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 9:46:09 PM Β· Difficulty 11.5686 Β· 4,202,894 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
abef676c6cdc3dce688cb3cf1ddf48e020cb9e2e950849b5cef61cfba870829b
View on Chainz β†—

Difficulty

11.568557

Transactions

1

Size

201 B

Version

2

Bits

0b918cf8

Nonce

98,617,134

Timestamp

4/30/2018, 9:46:09 PM

Confirmations

4,202,894

Merkle Root

33f7759ff8282b471446d9f10a3c1d6691af15ba9dabcfe669b1d047b1cdaf45
Transactions (1)
Coinbase33f7759ff8282b…b1d047b1cdaf45
1 in β†’ 1 out7.4600 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.

2.266 Γ— 10⁹⁷(98-digit number)
22662841044483065665…07096768495547842560
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
2.266 Γ— 10⁹⁷(98-digit number)
22662841044483065665…07096768495547842561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.532 Γ— 10⁹⁷(98-digit number)
45325682088966131330…14193536991095685121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.065 Γ— 10⁹⁷(98-digit number)
90651364177932262661…28387073982191370241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.813 Γ— 10⁹⁸(99-digit number)
18130272835586452532…56774147964382740481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.626 Γ— 10⁹⁸(99-digit number)
36260545671172905064…13548295928765480961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.252 Γ— 10⁹⁸(99-digit number)
72521091342345810129…27096591857530961921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.450 Γ— 10⁹⁹(100-digit number)
14504218268469162025…54193183715061923841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.900 Γ— 10⁹⁹(100-digit number)
29008436536938324051…08386367430123847681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.801 Γ— 10⁹⁹(100-digit number)
58016873073876648103…16772734860247695361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.160 Γ— 10¹⁰⁰(101-digit number)
11603374614775329620…33545469720495390721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.320 Γ— 10¹⁰⁰(101-digit number)
23206749229550659241…67090939440990781441
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 2640142

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 abef676c6cdc3dce688cb3cf1ddf48e020cb9e2e950849b5cef61cfba870829b

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 #2,640,142 on Chainz β†—
Circulating Supply:57,988,644 XPMΒ·at block #6,843,035 Β· updates every 60s
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