XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,818,211

Block #2,818,211

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/31/2018, 9:27:42 AM Β· Difficulty 11.6970 Β· 4,026,595 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6c51e25d3fcf337e932c0c5af71d1e4893bb9e4f2d6fae36e66cb319cf4f2c6f
View on Chainz β†—

Difficulty

11.696991

Transactions

1

Size

200 B

Version

2

Bits

0bb26dfc

Nonce

1,116,796,828

Timestamp

8/31/2018, 9:27:42 AM

Confirmations

4,026,595

Merkle Root

6b15626a2572da23d11006b0222e18b524cffee3c8f476f7ae11dcabdd1b9d28
Transactions (1)
Coinbase6b15626a2572da…11dcabdd1b9d28
1 in β†’ 1 out7.3000 XPM110 B
AHcX1We5…P5yCUYhG
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.

7.708 Γ— 10⁹⁡(96-digit number)
77085478641730362992…49703362061036369920
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
7.708 Γ— 10⁹⁡(96-digit number)
77085478641730362992…49703362061036369919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.541 Γ— 10⁹⁢(97-digit number)
15417095728346072598…99406724122072739839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.083 Γ— 10⁹⁢(97-digit number)
30834191456692145197…98813448244145479679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.166 Γ— 10⁹⁢(97-digit number)
61668382913384290394…97626896488290959359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.233 Γ— 10⁹⁷(98-digit number)
12333676582676858078…95253792976581918719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.466 Γ— 10⁹⁷(98-digit number)
24667353165353716157…90507585953163837439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.933 Γ— 10⁹⁷(98-digit number)
49334706330707432315…81015171906327674879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.866 Γ— 10⁹⁷(98-digit number)
98669412661414864630…62030343812655349759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.973 Γ— 10⁹⁸(99-digit number)
19733882532282972926…24060687625310699519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.946 Γ— 10⁹⁸(99-digit number)
39467765064565945852…48121375250621399039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.893 Γ— 10⁹⁸(99-digit number)
78935530129131891704…96242750501242798079
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 2818211

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 6c51e25d3fcf337e932c0c5af71d1e4893bb9e4f2d6fae36e66cb319cf4f2c6f

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 #2,818,211 on Chainz β†—
Circulating Supply:58,002,864 XPMΒ·at block #6,844,805 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