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Home/Chain Registry/Block #2,833,072

Block #2,833,072

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 12:13:43 PM Β· Difficulty 11.7147 Β· 4,011,987 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b573270a6dfcae9f3738a0995bea6530ab4b54bdd593a4da8acaf1a2a88b4e1c
View on Chainz β†—

Difficulty

11.714656

Transactions

1

Size

200 B

Version

2

Bits

0bb6f3b3

Nonce

495,803,632

Timestamp

9/10/2018, 12:13:43 PM

Confirmations

4,011,987

Merkle Root

db27205dd5e74d6dd1a0ea98724cca448788f178d0dd8851db857b962856010e
Transactions (1)
Coinbasedb27205dd5e74d…857b962856010e
1 in β†’ 1 out7.2700 XPM110 B
AezsbRVd…so7Fn8gV
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.

5.645 Γ— 10⁹⁡(96-digit number)
56451146033262281319…50661795357576710000
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
5.645 Γ— 10⁹⁡(96-digit number)
56451146033262281319…50661795357576710001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.129 Γ— 10⁹⁢(97-digit number)
11290229206652456263…01323590715153420001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.258 Γ— 10⁹⁢(97-digit number)
22580458413304912527…02647181430306840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.516 Γ— 10⁹⁢(97-digit number)
45160916826609825055…05294362860613680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.032 Γ— 10⁹⁢(97-digit number)
90321833653219650110…10588725721227360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.806 Γ— 10⁹⁷(98-digit number)
18064366730643930022…21177451442454720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.612 Γ— 10⁹⁷(98-digit number)
36128733461287860044…42354902884909440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.225 Γ— 10⁹⁷(98-digit number)
72257466922575720088…84709805769818880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.445 Γ— 10⁹⁸(99-digit number)
14451493384515144017…69419611539637760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.890 Γ— 10⁹⁸(99-digit number)
28902986769030288035…38839223079275520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.780 Γ— 10⁹⁸(99-digit number)
57805973538060576071…77678446158551040001
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 2833072

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 b573270a6dfcae9f3738a0995bea6530ab4b54bdd593a4da8acaf1a2a88b4e1c

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 #2,833,072 on Chainz β†—
Circulating Supply:58,004,896 XPMΒ·at block #6,845,058 Β· updates every 60s
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