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Home/Chain Registry/Block #343,764

Block #343,764

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/4/2014, 9:15:50 PM Β· Difficulty 10.1848 Β· 6,499,631 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cd08c5da1bb01e80adf5f7ad7148d1eca0f32dcc4755c0017c4f7ae2cd729968
View on Chainz β†—

Height

#343,764

Difficulty

10.184823

Transactions

1

Size

206 B

Version

2

Bits

0a2f508f

Nonce

184,550,031

Timestamp

1/4/2014, 9:15:50 PM

Confirmations

6,499,631

Merkle Root

47127fc9e1fdb85434937caabda642d118c9431ce3044cf9fcb3b3c52851344f
Transactions (1)
Coinbase47127fc9e1fdb8…b3b3c52851344f
1 in β†’ 1 out9.6300 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.

2.858 Γ— 10⁹⁡(96-digit number)
28583308768687744201…88533834524028545520
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
2.858 Γ— 10⁹⁡(96-digit number)
28583308768687744201…88533834524028545519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.716 Γ— 10⁹⁡(96-digit number)
57166617537375488402…77067669048057091039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.143 Γ— 10⁹⁢(97-digit number)
11433323507475097680…54135338096114182079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.286 Γ— 10⁹⁢(97-digit number)
22866647014950195360…08270676192228364159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.573 Γ— 10⁹⁢(97-digit number)
45733294029900390721…16541352384456728319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.146 Γ— 10⁹⁢(97-digit number)
91466588059800781443…33082704768913456639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.829 Γ— 10⁹⁷(98-digit number)
18293317611960156288…66165409537826913279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.658 Γ— 10⁹⁷(98-digit number)
36586635223920312577…32330819075653826559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.317 Γ— 10⁹⁷(98-digit number)
73173270447840625154…64661638151307653119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.463 Γ— 10⁹⁸(99-digit number)
14634654089568125030…29323276302615306239
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 343764

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 cd08c5da1bb01e80adf5f7ad7148d1eca0f32dcc4755c0017c4f7ae2cd729968

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 #343,764 on Chainz β†—
Circulating Supply:57,991,524 XPMΒ·at block #6,843,394 Β· updates every 60s
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