XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,335,198

Block #3,335,198

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2019, 5:25:23 PM Β· Difficulty 11.0023 Β· 3,508,604 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
77fed5b401fa22bf088a77240d9639f3bbbaef167cadb3bfca31fc7dde3d9298
View on Chainz β†—

Difficulty

11.002283

Transactions

1

Size

200 B

Version

2

Bits

0b0095a3

Nonce

748,484,409

Timestamp

8/31/2019, 5:25:23 PM

Confirmations

3,508,604

Merkle Root

3e694dd37b10ac9b52c604ced370fe5b88b4392525b24274162c4cc8536ec261
Transactions (1)
Coinbase3e694dd37b10ac…2c4cc8536ec261
1 in β†’ 1 out8.2500 XPM110 B
AXfJqzUb…HXeXmjMz
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.

4.671 Γ— 10⁹⁴(95-digit number)
46712899557833507959…81075593128515647200
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
4.671 Γ— 10⁹⁴(95-digit number)
46712899557833507959…81075593128515647199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.342 Γ— 10⁹⁴(95-digit number)
93425799115667015919…62151186257031294399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.868 Γ— 10⁹⁡(96-digit number)
18685159823133403183…24302372514062588799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.737 Γ— 10⁹⁡(96-digit number)
37370319646266806367…48604745028125177599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.474 Γ— 10⁹⁡(96-digit number)
74740639292533612735…97209490056250355199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.494 Γ— 10⁹⁢(97-digit number)
14948127858506722547…94418980112500710399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.989 Γ— 10⁹⁢(97-digit number)
29896255717013445094…88837960225001420799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.979 Γ— 10⁹⁢(97-digit number)
59792511434026890188…77675920450002841599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.195 Γ— 10⁹⁷(98-digit number)
11958502286805378037…55351840900005683199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.391 Γ— 10⁹⁷(98-digit number)
23917004573610756075…10703681800011366399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.783 Γ— 10⁹⁷(98-digit number)
47834009147221512150…21407363600022732799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3335198

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 77fed5b401fa22bf088a77240d9639f3bbbaef167cadb3bfca31fc7dde3d9298

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 #3,335,198 on Chainz β†—
Circulating Supply:57,994,793 XPMΒ·at block #6,843,801 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy