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Block #191,858

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/3/2013, 11:01:26 AM Β· Difficulty 9.8751 Β· 6,603,986 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
192a1aec81d494b0964ddf3cfd7fae4ef56d00f44d8cb4517acf43baf767acdb
View on Chainz β†—

Height

#191,858

Difficulty

9.875138

Transactions

1

Size

206 B

Version

2

Bits

09e0090e

Nonce

1,984

Timestamp

10/3/2013, 11:01:26 AM

Confirmations

6,603,986

Merkle Root

bf7a9e0781701cd883c1d904aefab90ccaec3b5f7159686f0d26029477637662
Transactions (1)
Coinbasebf7a9e0781701c…26029477637662
1 in β†’ 1 out10.2400 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.546 Γ— 10⁹³(94-digit number)
45469669767399204980…00477091717056089600
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
4.546 Γ— 10⁹³(94-digit number)
45469669767399204980…00477091717056089599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.093 Γ— 10⁹³(94-digit number)
90939339534798409960…00954183434112179199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.818 Γ— 10⁹⁴(95-digit number)
18187867906959681992…01908366868224358399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.637 Γ— 10⁹⁴(95-digit number)
36375735813919363984…03816733736448716799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.275 Γ— 10⁹⁴(95-digit number)
72751471627838727968…07633467472897433599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.455 Γ— 10⁹⁡(96-digit number)
14550294325567745593…15266934945794867199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.910 Γ— 10⁹⁡(96-digit number)
29100588651135491187…30533869891589734399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.820 Γ— 10⁹⁡(96-digit number)
58201177302270982374…61067739783179468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁢(97-digit number)
11640235460454196474…22135479566358937599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 191858

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 192a1aec81d494b0964ddf3cfd7fae4ef56d00f44d8cb4517acf43baf767acdb

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 #191,858 on Chainz β†—
Circulating Supply:57,610,836 XPMΒ·at block #6,795,843 Β· updates every 60s
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