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Home/Chain Registry/Block #2,333,330

Block #2,333,330

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2017, 3:04:25 AM Β· Difficulty 10.9230 Β· 4,511,698 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dd03cac89c074d2ba7b66bc4ea5b483480aefc400a17af57ff4a75f0a6da89da
View on Chainz β†—

Difficulty

10.922966

Transactions

1

Size

199 B

Version

2

Bits

0aec4787

Nonce

1,308,790,628

Timestamp

10/12/2017, 3:04:25 AM

Confirmations

4,511,698

Merkle Root

bfa81a8443a918624c2b308f75bcb6ccc414d80a53fa1c051803395253473940
Transactions (1)
Coinbasebfa81a8443a918…03395253473940
1 in β†’ 1 out8.3700 XPM110 B
ARd3bjwj…VAVE8DUp
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.

2.737 Γ— 10⁹²(93-digit number)
27371997928811988645…35762617152546935680
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
2.737 Γ— 10⁹²(93-digit number)
27371997928811988645…35762617152546935681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.474 Γ— 10⁹²(93-digit number)
54743995857623977291…71525234305093871361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.094 Γ— 10⁹³(94-digit number)
10948799171524795458…43050468610187742721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.189 Γ— 10⁹³(94-digit number)
21897598343049590916…86100937220375485441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.379 Γ— 10⁹³(94-digit number)
43795196686099181832…72201874440750970881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.759 Γ— 10⁹³(94-digit number)
87590393372198363665…44403748881501941761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.751 Γ— 10⁹⁴(95-digit number)
17518078674439672733…88807497763003883521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.503 Γ— 10⁹⁴(95-digit number)
35036157348879345466…77614995526007767041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.007 Γ— 10⁹⁴(95-digit number)
70072314697758690932…55229991052015534081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.401 Γ— 10⁹⁡(96-digit number)
14014462939551738186…10459982104031068161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2333330

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 dd03cac89c074d2ba7b66bc4ea5b483480aefc400a17af57ff4a75f0a6da89da

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 #2,333,330 on Chainz β†—
Circulating Supply:58,004,649 XPMΒ·at block #6,845,027 Β· updates every 60s
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