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Home/Chain Registry/Block #2,643,932

Block #2,643,932

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 7:08:44 AM Β· Difficulty 11.6975 Β· 4,188,631 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dace7204f7e414be270cb9dc3e3345b431f95277bd1b39247d6fbad7bf09f2fc
View on Chainz β†—

Difficulty

11.697452

Transactions

1

Size

201 B

Version

2

Bits

0bb28c3b

Nonce

1,764,154,485

Timestamp

5/2/2018, 7:08:44 AM

Confirmations

4,188,631

Merkle Root

9abe455cabed7b5a440ba26c1904ee79bee0c15306fa42fc91e313b6481f2dba
Transactions (1)
Coinbase9abe455cabed7b…e313b6481f2dba
1 in β†’ 1 out7.3000 XPM110 B
ANnJCVA1…f6QeB5sh
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.

2.015 Γ— 10⁹⁷(98-digit number)
20151172920192644571…78230452494969241600
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
2.015 Γ— 10⁹⁷(98-digit number)
20151172920192644571…78230452494969241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.030 Γ— 10⁹⁷(98-digit number)
40302345840385289142…56460904989938483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.060 Γ— 10⁹⁷(98-digit number)
80604691680770578284…12921809979876966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.612 Γ— 10⁹⁸(99-digit number)
16120938336154115656…25843619959753932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.224 Γ— 10⁹⁸(99-digit number)
32241876672308231313…51687239919507865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.448 Γ— 10⁹⁸(99-digit number)
64483753344616462627…03374479839015731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.289 Γ— 10⁹⁹(100-digit number)
12896750668923292525…06748959678031462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.579 Γ— 10⁹⁹(100-digit number)
25793501337846585050…13497919356062924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.158 Γ— 10⁹⁹(100-digit number)
51587002675693170101…26995838712125849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.031 Γ— 10¹⁰⁰(101-digit number)
10317400535138634020…53991677424251699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.063 Γ— 10¹⁰⁰(101-digit number)
20634801070277268040…07983354848503398401
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 2643932

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 dace7204f7e414be270cb9dc3e3345b431f95277bd1b39247d6fbad7bf09f2fc

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 #2,643,932 on Chainz β†—
Circulating Supply:57,904,661 XPMΒ·at block #6,832,562 Β· updates every 60s
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