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Block #344,706

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/5/2014, 11:23:35 AM Β· Difficulty 10.2005 Β· 6,455,425 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f52722782c59188f4e4bc41ff144bf9ea5cff09682793139ff33c7bcad075cb3
View on Chainz β†—

Height

#344,706

Difficulty

10.200493

Transactions

1

Size

205 B

Version

2

Bits

0a33538a

Nonce

232,394

Timestamp

1/5/2014, 11:23:35 AM

Confirmations

6,455,425

Merkle Root

dc90b09c2c86913c5fb6591a90579a68fac1db8355cfb0eb66f4ca2760d0981c
Transactions (1)
Coinbasedc90b09c2c8691…f4ca2760d0981c
1 in β†’ 1 out9.6000 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.

1.708 Γ— 10⁹³(94-digit number)
17084423633918277523…89741365310373867040
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
1.708 Γ— 10⁹³(94-digit number)
17084423633918277523…89741365310373867039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.416 Γ— 10⁹³(94-digit number)
34168847267836555047…79482730620747734079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.833 Γ— 10⁹³(94-digit number)
68337694535673110095…58965461241495468159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.366 Γ— 10⁹⁴(95-digit number)
13667538907134622019…17930922482990936319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.733 Γ— 10⁹⁴(95-digit number)
27335077814269244038…35861844965981872639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.467 Γ— 10⁹⁴(95-digit number)
54670155628538488076…71723689931963745279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁡(96-digit number)
10934031125707697615…43447379863927490559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.186 Γ— 10⁹⁡(96-digit number)
21868062251415395230…86894759727854981119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.373 Γ— 10⁹⁡(96-digit number)
43736124502830790460…73789519455709962239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.747 Γ— 10⁹⁡(96-digit number)
87472249005661580921…47579038911419924479
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 344706

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 f52722782c59188f4e4bc41ff144bf9ea5cff09682793139ff33c7bcad075cb3

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 #344,706 on Chainz β†—
Circulating Supply:57,645,109 XPMΒ·at block #6,800,130 Β· updates every 60s
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