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Block #175,241

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/22/2013, 4:02:39 AM Β· Difficulty 9.8637 Β· 6,650,214 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ebfff38765088c70f9058e1cd9aeddbbfdb137510b7801c39e3ecba6141ddf70
View on Chainz β†—

Height

#175,241

Difficulty

9.863698

Transactions

1

Size

199 B

Version

2

Bits

09dd1b4d

Nonce

45,682

Timestamp

9/22/2013, 4:02:39 AM

Confirmations

6,650,214

Merkle Root

c2d46f4750184ae2d1b7e6541fe6445e3641579ead8c9f6ab0affda15ddbe2a5
Transactions (1)
Coinbasec2d46f4750184a…affda15ddbe2a5
1 in β†’ 1 out10.2600 XPM109 B
AHNdTz9R…DHU2jpcA
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.

6.608 Γ— 10⁹⁡(96-digit number)
66085935417692419400…19208131316783136000
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
6.608 Γ— 10⁹⁡(96-digit number)
66085935417692419400…19208131316783136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.321 Γ— 10⁹⁢(97-digit number)
13217187083538483880…38416262633566272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.643 Γ— 10⁹⁢(97-digit number)
26434374167076967760…76832525267132544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.286 Γ— 10⁹⁢(97-digit number)
52868748334153935520…53665050534265088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.057 Γ— 10⁹⁷(98-digit number)
10573749666830787104…07330101068530176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.114 Γ— 10⁹⁷(98-digit number)
21147499333661574208…14660202137060352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.229 Γ— 10⁹⁷(98-digit number)
42294998667323148416…29320404274120704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.458 Γ— 10⁹⁷(98-digit number)
84589997334646296832…58640808548241408001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.691 Γ— 10⁹⁸(99-digit number)
16917999466929259366…17281617096482816001
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 175241

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 ebfff38765088c70f9058e1cd9aeddbbfdb137510b7801c39e3ecba6141ddf70

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 #175,241 on Chainz β†—
Circulating Supply:57,847,744 XPMΒ·at block #6,825,454 Β· updates every 60s
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