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Block #445,930

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/16/2014, 5:30:31 AM Β· Difficulty 10.3594 Β· 6,380,982 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8f54f70c5cafcccffdd037d85ebb21aa5ce4f60c0c6bb0915e36b2e0a97f6479
View on Chainz β†—

Height

#445,930

Difficulty

10.359364

Transactions

1

Size

200 B

Version

2

Bits

0a5bff45

Nonce

77,322

Timestamp

3/16/2014, 5:30:31 AM

Confirmations

6,380,982

Merkle Root

478e9ee4be41beea51044782646660ad72b21559f2772cec4a85dcbd180c4b67
Transactions (1)
Coinbase478e9ee4be41be…85dcbd180c4b67
1 in β†’ 1 out9.3000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.535 Γ— 10⁹⁴(95-digit number)
35355832324951156701…28841153559536336000
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
3.535 Γ— 10⁹⁴(95-digit number)
35355832324951156701…28841153559536335999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.071 Γ— 10⁹⁴(95-digit number)
70711664649902313402…57682307119072671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.414 Γ— 10⁹⁡(96-digit number)
14142332929980462680…15364614238145343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.828 Γ— 10⁹⁡(96-digit number)
28284665859960925360…30729228476290687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.656 Γ— 10⁹⁡(96-digit number)
56569331719921850721…61458456952581375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.131 Γ— 10⁹⁢(97-digit number)
11313866343984370144…22916913905162751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.262 Γ— 10⁹⁢(97-digit number)
22627732687968740288…45833827810325503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.525 Γ— 10⁹⁢(97-digit number)
45255465375937480577…91667655620651007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.051 Γ— 10⁹⁢(97-digit number)
90510930751874961154…83335311241302015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.810 Γ— 10⁹⁷(98-digit number)
18102186150374992230…66670622482604031999
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 445930

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 8f54f70c5cafcccffdd037d85ebb21aa5ce4f60c0c6bb0915e36b2e0a97f6479

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 #445,930 on Chainz β†—
Circulating Supply:57,859,465 XPMΒ·at block #6,826,911 Β· updates every 60s
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