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Home/Chain Registry/Block #2,640,081

Block #2,640,081

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 9:13:29 PM Β· Difficulty 11.5661 Β· 4,198,224 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
05f9c1fba5a649f3880d0226024bb406ef3de7db7a8ab50c310dcd5876592a6a
View on Chainz β†—

Difficulty

11.566096

Transactions

1

Size

202 B

Version

2

Bits

0b90eba9

Nonce

9,758,096

Timestamp

4/30/2018, 9:13:29 PM

Confirmations

4,198,224

Merkle Root

784eef7d0d6da4cf54deed78531e9a34eaf323a1750ede2e34bf154df44b5974
Transactions (1)
Coinbase784eef7d0d6da4…bf154df44b5974
1 in β†’ 1 out7.4600 XPM110 B
ARF1cLs5…KyxuZ3UE
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.

2.216 Γ— 10⁹⁹(100-digit number)
22165030135500165212…67936168822176153600
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
2.216 Γ— 10⁹⁹(100-digit number)
22165030135500165212…67936168822176153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.433 Γ— 10⁹⁹(100-digit number)
44330060271000330425…35872337644352307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.866 Γ— 10⁹⁹(100-digit number)
88660120542000660850…71744675288704614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.773 Γ— 10¹⁰⁰(101-digit number)
17732024108400132170…43489350577409228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.546 Γ— 10¹⁰⁰(101-digit number)
35464048216800264340…86978701154818457601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.092 Γ— 10¹⁰⁰(101-digit number)
70928096433600528680…73957402309636915201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.418 Γ— 10¹⁰¹(102-digit number)
14185619286720105736…47914804619273830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.837 Γ— 10¹⁰¹(102-digit number)
28371238573440211472…95829609238547660801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.674 Γ— 10¹⁰¹(102-digit number)
56742477146880422944…91659218477095321601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.134 Γ— 10¹⁰²(103-digit number)
11348495429376084588…83318436954190643201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.269 Γ— 10¹⁰²(103-digit number)
22696990858752169177…66636873908381286401
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 2640081

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 05f9c1fba5a649f3880d0226024bb406ef3de7db7a8ab50c310dcd5876592a6a

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 #2,640,081 on Chainz β†—
Circulating Supply:57,950,714 XPMΒ·at block #6,838,304 Β· updates every 60s
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