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Block #192,708

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/4/2013, 1:34:00 AM Β· Difficulty 9.8746 Β· 6,603,182 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9aa993f34ae9da9ccd2be5ebbfd2ec3000663407dd10d6ac640f14b132025c93
View on Chainz β†—

Height

#192,708

Difficulty

9.874634

Transactions

1

Size

206 B

Version

2

Bits

09dfe803

Nonce

50,338,549

Timestamp

10/4/2013, 1:34:00 AM

Confirmations

6,603,182

Merkle Root

2bc32e5db9f5713666836bb9a2ad18621695b3f4eb76b7741c074456f2368b0d
Transactions (1)
Coinbase2bc32e5db9f571…074456f2368b0d
1 in β†’ 1 out10.2400 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.495 Γ— 10⁹³(94-digit number)
54957201116141111514…03945608905813737600
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
5.495 Γ— 10⁹³(94-digit number)
54957201116141111514…03945608905813737601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.099 Γ— 10⁹⁴(95-digit number)
10991440223228222302…07891217811627475201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.198 Γ— 10⁹⁴(95-digit number)
21982880446456444605…15782435623254950401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.396 Γ— 10⁹⁴(95-digit number)
43965760892912889211…31564871246509900801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.793 Γ— 10⁹⁴(95-digit number)
87931521785825778422…63129742493019801601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.758 Γ— 10⁹⁡(96-digit number)
17586304357165155684…26259484986039603201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.517 Γ— 10⁹⁡(96-digit number)
35172608714330311369…52518969972079206401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.034 Γ— 10⁹⁡(96-digit number)
70345217428660622738…05037939944158412801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.406 Γ— 10⁹⁢(97-digit number)
14069043485732124547…10075879888316825601
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 192708

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 9aa993f34ae9da9ccd2be5ebbfd2ec3000663407dd10d6ac640f14b132025c93

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 #192,708 on Chainz β†—
Circulating Supply:57,611,204 XPMΒ·at block #6,795,889 Β· updates every 60s
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