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Block #446,857

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/16/2014, 8:59:08 PM Β· Difficulty 10.3594 Β· 6,353,508 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
91a57f348f6e336583797617e027da2a7cd985d0109b33d4b64d7a4e33f84cad
View on Chainz β†—

Height

#446,857

Difficulty

10.359358

Transactions

1

Size

201 B

Version

2

Bits

0a5bfee5

Nonce

53,604

Timestamp

3/16/2014, 8:59:08 PM

Confirmations

6,353,508

Merkle Root

a047ee9190e85c61e5b4246f87448668c24f4b40b3a0527a980365885b0f28b6
Transactions (1)
Coinbasea047ee9190e85c…0365885b0f28b6
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.

1.101 Γ— 10⁹⁢(97-digit number)
11017376187841173357…08118403342827900160
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
1.101 Γ— 10⁹⁢(97-digit number)
11017376187841173357…08118403342827900159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.203 Γ— 10⁹⁢(97-digit number)
22034752375682346715…16236806685655800319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.406 Γ— 10⁹⁢(97-digit number)
44069504751364693431…32473613371311600639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.813 Γ— 10⁹⁢(97-digit number)
88139009502729386862…64947226742623201279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.762 Γ— 10⁹⁷(98-digit number)
17627801900545877372…29894453485246402559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.525 Γ— 10⁹⁷(98-digit number)
35255603801091754744…59788906970492805119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.051 Γ— 10⁹⁷(98-digit number)
70511207602183509489…19577813940985610239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.410 Γ— 10⁹⁸(99-digit number)
14102241520436701897…39155627881971220479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.820 Γ— 10⁹⁸(99-digit number)
28204483040873403795…78311255763942440959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.640 Γ— 10⁹⁸(99-digit number)
56408966081746807591…56622511527884881919
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 446857

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 91a57f348f6e336583797617e027da2a7cd985d0109b33d4b64d7a4e33f84cad

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 #446,857 on Chainz β†—
Circulating Supply:57,646,979 XPMΒ·at block #6,800,364 Β· updates every 60s
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