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Block #930

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/8/2013, 5:58:30 AM Β· Difficulty 7.0474 Β· 6,815,125 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
40101e7104745ee10a3210d8f9870cf37ed9ae374839bb0bfdc5ab87fdaaa2ba
View on Chainz β†—

Height

#930

Difficulty

7.047427

Transactions

1

Size

200 B

Version

2

Bits

070c2429

Nonce

447

Timestamp

7/8/2013, 5:58:30 AM

Confirmations

6,815,125

Merkle Root

98eb624846e1b591a42dfdef2a216dc01317895f8aa35df0f0ac2c5a5552b90c
Transactions (1)
Coinbase98eb624846e1b5…ac2c5a5552b90c
1 in β†’ 1 out20.1100 XPM108 B
ASgi6R1L…pAA9z2hc
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.

8.290 Γ— 10⁹⁹(100-digit number)
82907125661799428730…15500715595910864230
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
8.290 Γ— 10⁹⁹(100-digit number)
82907125661799428730…15500715595910864231
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.658 Γ— 10¹⁰⁰(101-digit number)
16581425132359885746…31001431191821728461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.316 Γ— 10¹⁰⁰(101-digit number)
33162850264719771492…62002862383643456921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.632 Γ— 10¹⁰⁰(101-digit number)
66325700529439542984…24005724767286913841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.326 Γ— 10¹⁰¹(102-digit number)
13265140105887908596…48011449534573827681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.653 Γ— 10¹⁰¹(102-digit number)
26530280211775817193…96022899069147655361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.306 Γ— 10¹⁰¹(102-digit number)
53060560423551634387…92045798138295310721
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 930

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 40101e7104745ee10a3210d8f9870cf37ed9ae374839bb0bfdc5ab87fdaaa2ba

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 #930 on Chainz β†—
Circulating Supply:57,772,555 XPMΒ·at block #6,816,054 Β· updates every 60s
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