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Block #202,672

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/10/2013, 9:12:51 AM Β· Difficulty 9.8954 Β· 6,597,684 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7ef016b5c2f5f798e936b570fc212841f0aa0039e4667dd87a0dee25f58ffe58
View on Chainz β†—

Height

#202,672

Difficulty

9.895370

Transactions

1

Size

201 B

Version

2

Bits

09e536f6

Nonce

394,633

Timestamp

10/10/2013, 9:12:51 AM

Confirmations

6,597,684

Merkle Root

0daac2dd0c0362214e70d1e6842c6216029ecd1cde22c00aad0ba481a678bc63
Transactions (1)
Coinbase0daac2dd0c0362…0ba481a678bc63
1 in β†’ 1 out10.2000 XPM110 B
ANvtpRa1…QjsraDJz
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.

1.411 Γ— 10⁹⁸(99-digit number)
14113606082667495040…60928458618277766400
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
1.411 Γ— 10⁹⁸(99-digit number)
14113606082667495040…60928458618277766401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.822 Γ— 10⁹⁸(99-digit number)
28227212165334990080…21856917236555532801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.645 Γ— 10⁹⁸(99-digit number)
56454424330669980160…43713834473111065601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.129 Γ— 10⁹⁹(100-digit number)
11290884866133996032…87427668946222131201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.258 Γ— 10⁹⁹(100-digit number)
22581769732267992064…74855337892444262401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.516 Γ— 10⁹⁹(100-digit number)
45163539464535984128…49710675784888524801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.032 Γ— 10⁹⁹(100-digit number)
90327078929071968257…99421351569777049601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.806 Γ— 10¹⁰⁰(101-digit number)
18065415785814393651…98842703139554099201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.613 Γ— 10¹⁰⁰(101-digit number)
36130831571628787302…97685406279108198401
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 202672

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 7ef016b5c2f5f798e936b570fc212841f0aa0039e4667dd87a0dee25f58ffe58

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 #202,672 on Chainz β†—
Circulating Supply:57,646,905 XPMΒ·at block #6,800,355 Β· updates every 60s
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