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Home/Chain Registry/Block #349,766

Block #349,766

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/8/2014, 2:50:23 PM Β· Difficulty 10.2815 Β· 6,451,144 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
877da69ae07cb7575d4e1f2247c1ac832066b94602e7c48e44376e1dac143fbb
View on Chainz β†—

Height

#349,766

Difficulty

10.281454

Transactions

1

Size

206 B

Version

2

Bits

0a480d64

Nonce

201,332,622

Timestamp

1/8/2014, 2:50:23 PM

Confirmations

6,451,144

Merkle Root

452b794a41d3c10e47709ecee77556516c57b25d88f237afc4f836212b9686f0
Transactions (1)
Coinbase452b794a41d3c1…f836212b9686f0
1 in β†’ 1 out9.4500 XPM116 B
AbwWkWZt…kawDhufa
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.

1.703 Γ— 10⁹⁡(96-digit number)
17034766517415329002…94079479277653055120
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
1.703 Γ— 10⁹⁡(96-digit number)
17034766517415329002…94079479277653055119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.406 Γ— 10⁹⁡(96-digit number)
34069533034830658005…88158958555306110239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.813 Γ— 10⁹⁡(96-digit number)
68139066069661316011…76317917110612220479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.362 Γ— 10⁹⁢(97-digit number)
13627813213932263202…52635834221224440959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.725 Γ— 10⁹⁢(97-digit number)
27255626427864526404…05271668442448881919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.451 Γ— 10⁹⁢(97-digit number)
54511252855729052809…10543336884897763839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.090 Γ— 10⁹⁷(98-digit number)
10902250571145810561…21086673769795527679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.180 Γ— 10⁹⁷(98-digit number)
21804501142291621123…42173347539591055359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.360 Γ— 10⁹⁷(98-digit number)
43609002284583242247…84346695079182110719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.721 Γ— 10⁹⁷(98-digit number)
87218004569166484495…68693390158364221439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 349766

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 877da69ae07cb7575d4e1f2247c1ac832066b94602e7c48e44376e1dac143fbb

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 #349,766 on Chainz β†—
Circulating Supply:57,651,341 XPMΒ·at block #6,800,909 Β· updates every 60s
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