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Block #175,358

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/22/2013, 6:02:26 AM Β· Difficulty 9.8636 Β· 6,640,814 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b22f60dbeb8f327fe24d993046bc2e2c3be52e36bdc85ec5d326d9e35bcb79d3
View on Chainz β†—

Height

#175,358

Difficulty

9.863630

Transactions

1

Size

199 B

Version

2

Bits

09dd16dd

Nonce

32,180

Timestamp

9/22/2013, 6:02:26 AM

Confirmations

6,640,814

Merkle Root

c870db305036894a29022db7bf41eaf41228c9a4e819f85101f848d63131eb8e
Transactions (1)
Coinbasec870db30503689…f848d63131eb8e
1 in β†’ 1 out10.2600 XPM109 B
AM1A9CZL…as4Lpogj
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.

2.305 Γ— 10⁹⁴(95-digit number)
23053251152310025397…20120140032150393600
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
2.305 Γ— 10⁹⁴(95-digit number)
23053251152310025397…20120140032150393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.610 Γ— 10⁹⁴(95-digit number)
46106502304620050795…40240280064300787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.221 Γ— 10⁹⁴(95-digit number)
92213004609240101590…80480560128601574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.844 Γ— 10⁹⁡(96-digit number)
18442600921848020318…60961120257203148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.688 Γ— 10⁹⁡(96-digit number)
36885201843696040636…21922240514406297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.377 Γ— 10⁹⁡(96-digit number)
73770403687392081272…43844481028812595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.475 Γ— 10⁹⁢(97-digit number)
14754080737478416254…87688962057625190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.950 Γ— 10⁹⁢(97-digit number)
29508161474956832508…75377924115250380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.901 Γ— 10⁹⁢(97-digit number)
59016322949913665017…50755848230500761601
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 175358

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 b22f60dbeb8f327fe24d993046bc2e2c3be52e36bdc85ec5d326d9e35bcb79d3

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 #175,358 on Chainz β†—
Circulating Supply:57,773,500 XPMΒ·at block #6,816,171 Β· updates every 60s
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