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Home/Chain Registry/Block #1,894,123

Block #1,894,123

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/14/2016, 6:49:32 PM Β· Difficulty 10.7445 Β· 4,943,649 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0293f9017079b840e96a4034bf1360454fab8f1f491a0e047bff48d2a57279cd
View on Chainz β†—

Difficulty

10.744490

Transactions

1

Size

200 B

Version

2

Bits

0abe96e2

Nonce

1,057,351,882

Timestamp

12/14/2016, 6:49:32 PM

Confirmations

4,943,649

Merkle Root

285f4b3affa1a1224e9d8958bcd687774accd977783245c99ca98b429e61c9d3
Transactions (1)
Coinbase285f4b3affa1a1…a98b429e61c9d3
1 in β†’ 1 out8.6500 XPM110 B
AP7ySHfz…1zLY5pEC
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.

2.242 Γ— 10⁹⁴(95-digit number)
22429082180312931750…84173382332590489600
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
2.242 Γ— 10⁹⁴(95-digit number)
22429082180312931750…84173382332590489599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.485 Γ— 10⁹⁴(95-digit number)
44858164360625863501…68346764665180979199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.971 Γ— 10⁹⁴(95-digit number)
89716328721251727003…36693529330361958399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.794 Γ— 10⁹⁡(96-digit number)
17943265744250345400…73387058660723916799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.588 Γ— 10⁹⁡(96-digit number)
35886531488500690801…46774117321447833599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.177 Γ— 10⁹⁡(96-digit number)
71773062977001381602…93548234642895667199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.435 Γ— 10⁹⁢(97-digit number)
14354612595400276320…87096469285791334399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.870 Γ— 10⁹⁢(97-digit number)
28709225190800552641…74192938571582668799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.741 Γ— 10⁹⁢(97-digit number)
57418450381601105282…48385877143165337599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.148 Γ— 10⁹⁷(98-digit number)
11483690076320221056…96771754286330675199
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 1894123

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 0293f9017079b840e96a4034bf1360454fab8f1f491a0e047bff48d2a57279cd

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 #1,894,123 on Chainz β†—
Circulating Supply:57,946,511 XPMΒ·at block #6,837,771 Β· updates every 60s
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