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Block #190,328

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/2/2013, 10:32:20 AM Β· Difficulty 9.8734 Β· 6,609,834 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
29a55019c96650c11e26a4fbfc352d7fa46db6ff5d80a6f6805a19c5c02c0caa
View on Chainz β†—

Height

#190,328

Difficulty

9.873378

Transactions

1

Size

200 B

Version

2

Bits

09df95ad

Nonce

102,005

Timestamp

10/2/2013, 10:32:20 AM

Confirmations

6,609,834

Merkle Root

01de392eec1ea46ab35bf5d6d48354c60d8227c52a74ebbea0c75e45f6025498
Transactions (1)
Coinbase01de392eec1ea4…c75e45f6025498
1 in β†’ 1 out10.2400 XPM109 B
AHJtUwMe…CcBGZYoa
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.

1.882 Γ— 10⁹⁢(97-digit number)
18824469477568356538…34038980796739057440
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
1.882 Γ— 10⁹⁢(97-digit number)
18824469477568356538…34038980796739057441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.764 Γ— 10⁹⁢(97-digit number)
37648938955136713077…68077961593478114881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.529 Γ— 10⁹⁢(97-digit number)
75297877910273426155…36155923186956229761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.505 Γ— 10⁹⁷(98-digit number)
15059575582054685231…72311846373912459521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.011 Γ— 10⁹⁷(98-digit number)
30119151164109370462…44623692747824919041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.023 Γ— 10⁹⁷(98-digit number)
60238302328218740924…89247385495649838081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.204 Γ— 10⁹⁸(99-digit number)
12047660465643748184…78494770991299676161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.409 Γ— 10⁹⁸(99-digit number)
24095320931287496369…56989541982599352321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.819 Γ— 10⁹⁸(99-digit number)
48190641862574992739…13979083965198704641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 190328

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 29a55019c96650c11e26a4fbfc352d7fa46db6ff5d80a6f6805a19c5c02c0caa

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 #190,328 on Chainz β†—
Circulating Supply:57,645,362 XPMΒ·at block #6,800,161 Β· updates every 60s
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