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Block #191,967

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/3/2013, 1:02:07 PM Β· Difficulty 9.8749 Β· 6,633,427 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cbdc47525f8aa01d3cd6c4b598ca74d58ddaced37a1b9b51eefbe38ce923f8ab
View on Chainz β†—

Height

#191,967

Difficulty

9.874860

Transactions

1

Size

199 B

Version

2

Bits

09dff6cb

Nonce

128,188

Timestamp

10/3/2013, 1:02:07 PM

Confirmations

6,633,427

Merkle Root

5ebe0ea22820fbf43a8bcd0ac5f8ef29d96e069f413333dd21efd038c21a0945
Transactions (1)
Coinbase5ebe0ea22820fb…efd038c21a0945
1 in β†’ 1 out10.2400 XPM109 B
AHwvzr4f…DFN5Jb16
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.

6.961 Γ— 10⁹³(94-digit number)
69617774075404604382…89676650107235752960
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
6.961 Γ— 10⁹³(94-digit number)
69617774075404604382…89676650107235752959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁴(95-digit number)
13923554815080920876…79353300214471505919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.784 Γ— 10⁹⁴(95-digit number)
27847109630161841752…58706600428943011839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.569 Γ— 10⁹⁴(95-digit number)
55694219260323683505…17413200857886023679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁡(96-digit number)
11138843852064736701…34826401715772047359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.227 Γ— 10⁹⁡(96-digit number)
22277687704129473402…69652803431544094719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.455 Γ— 10⁹⁡(96-digit number)
44555375408258946804…39305606863088189439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.911 Γ— 10⁹⁡(96-digit number)
89110750816517893609…78611213726176378879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.782 Γ— 10⁹⁢(97-digit number)
17822150163303578721…57222427452352757759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.564 Γ— 10⁹⁢(97-digit number)
35644300326607157443…14444854904705515519
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 191967

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 cbdc47525f8aa01d3cd6c4b598ca74d58ddaced37a1b9b51eefbe38ce923f8ab

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 #191,967 on Chainz β†—
Circulating Supply:57,847,252 XPMΒ·at block #6,825,393 Β· updates every 60s
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