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Block #250,451

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/8/2013, 12:25:42 PM Β· Difficulty 9.9683 Β· 6,586,423 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1b9a662a266b0eccb50af36913e485af17acc2fe815614fcd39142a25172d353
View on Chainz β†—

Height

#250,451

Difficulty

9.968344

Transactions

1

Size

231 B

Version

2

Bits

09f7e55f

Nonce

3,237

Timestamp

11/8/2013, 12:25:42 PM

Confirmations

6,586,423

Merkle Root

f7bd4c638682d00f064cbcfae9a403f17224f4c2662a8f0808f571d711ff1e8c
Transactions (1)
Coinbasef7bd4c638682d0…f571d711ff1e8c
1 in β†’ 2 out10.0500 XPM140 B
AKcbk49N…GJbKa7j1AHsw4d6U…EnM8UXNZ
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.

8.771 Γ— 10⁹⁡(96-digit number)
87717348036163655200…18754028146892587400
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.771 Γ— 10⁹⁡(96-digit number)
87717348036163655200…18754028146892587399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.754 Γ— 10⁹⁢(97-digit number)
17543469607232731040…37508056293785174799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.508 Γ— 10⁹⁢(97-digit number)
35086939214465462080…75016112587570349599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.017 Γ— 10⁹⁢(97-digit number)
70173878428930924160…50032225175140699199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.403 Γ— 10⁹⁷(98-digit number)
14034775685786184832…00064450350281398399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.806 Γ— 10⁹⁷(98-digit number)
28069551371572369664…00128900700562796799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.613 Γ— 10⁹⁷(98-digit number)
56139102743144739328…00257801401125593599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.122 Γ— 10⁹⁸(99-digit number)
11227820548628947865…00515602802251187199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.245 Γ— 10⁹⁸(99-digit number)
22455641097257895731…01031205604502374399
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 250451

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 1b9a662a266b0eccb50af36913e485af17acc2fe815614fcd39142a25172d353

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 #250,451 on Chainz β†—
Circulating Supply:57,939,283 XPMΒ·at block #6,836,873 Β· updates every 60s
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