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Home/Chain Registry/Block #2,831,527

Block #2,831,527

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2018, 9:45:52 AM Β· Difficulty 11.7170 Β· 4,000,955 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
875d8037f9f5ee2ed86169819fe924050cd33463aa1b7dde95494962a865cc72
View on Chainz β†—

Difficulty

11.717019

Transactions

1

Size

201 B

Version

2

Bits

0bb78e91

Nonce

1,122,512,842

Timestamp

9/9/2018, 9:45:52 AM

Confirmations

4,000,955

Merkle Root

981ee6b8081d72c736a8e4d1eac113da5b7030b6142173dbfbd7ceb2d968153b
Transactions (1)
Coinbase981ee6b8081d72…d7ceb2d968153b
1 in β†’ 1 out7.2700 XPM110 B
AJJZMSaM…iFXEHXEZ
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.

4.428 Γ— 10⁹⁷(98-digit number)
44282310729613132545…88015271502409697280
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
4.428 Γ— 10⁹⁷(98-digit number)
44282310729613132545…88015271502409697281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.856 Γ— 10⁹⁷(98-digit number)
88564621459226265091…76030543004819394561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.771 Γ— 10⁹⁸(99-digit number)
17712924291845253018…52061086009638789121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.542 Γ— 10⁹⁸(99-digit number)
35425848583690506036…04122172019277578241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.085 Γ— 10⁹⁸(99-digit number)
70851697167381012073…08244344038555156481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.417 Γ— 10⁹⁹(100-digit number)
14170339433476202414…16488688077110312961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.834 Γ— 10⁹⁹(100-digit number)
28340678866952404829…32977376154220625921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.668 Γ— 10⁹⁹(100-digit number)
56681357733904809658…65954752308441251841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.133 Γ— 10¹⁰⁰(101-digit number)
11336271546780961931…31909504616882503681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.267 Γ— 10¹⁰⁰(101-digit number)
22672543093561923863…63819009233765007361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.534 Γ— 10¹⁰⁰(101-digit number)
45345086187123847727…27638018467530014721
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 2831527

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 875d8037f9f5ee2ed86169819fe924050cd33463aa1b7dde95494962a865cc72

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 #2,831,527 on Chainz β†—
Circulating Supply:57,904,009 XPMΒ·at block #6,832,481 Β· updates every 60s
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