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Home/Chain Registry/Block #197,922

Block #197,922

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/7/2013, 10:19:15 AM Β· Difficulty 9.8843 Β· 6,628,294 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
94b4fe74729b2222ef18c4fa3bb530aa569ab06d2d82b5e4b55f792a187d71dd
View on Chainz β†—

Height

#197,922

Difficulty

9.884304

Transactions

1

Size

205 B

Version

2

Bits

09e261b8

Nonce

2,481

Timestamp

10/7/2013, 10:19:15 AM

Confirmations

6,628,294

Merkle Root

ecc9513998d2eb09559cda70ee2fec93e4c4247057ca2da64060ee155e97714d
Transactions (1)
Coinbaseecc9513998d2eb…60ee155e97714d
1 in β†’ 1 out10.2200 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.

3.203 Γ— 10⁹³(94-digit number)
32039265074844005455…97251943954501836000
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
3.203 Γ— 10⁹³(94-digit number)
32039265074844005455…97251943954501835999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.407 Γ— 10⁹³(94-digit number)
64078530149688010911…94503887909003671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.281 Γ— 10⁹⁴(95-digit number)
12815706029937602182…89007775818007343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.563 Γ— 10⁹⁴(95-digit number)
25631412059875204364…78015551636014687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.126 Γ— 10⁹⁴(95-digit number)
51262824119750408729…56031103272029375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.025 Γ— 10⁹⁡(96-digit number)
10252564823950081745…12062206544058751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.050 Γ— 10⁹⁡(96-digit number)
20505129647900163491…24124413088117503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.101 Γ— 10⁹⁡(96-digit number)
41010259295800326983…48248826176235007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.202 Γ— 10⁹⁡(96-digit number)
82020518591600653967…96497652352470015999
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 197922

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 94b4fe74729b2222ef18c4fa3bb530aa569ab06d2d82b5e4b55f792a187d71dd

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 #197,922 on Chainz β†—
Circulating Supply:57,853,860 XPMΒ·at block #6,826,215 Β· updates every 60s
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