XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,991,556

Block #2,991,556

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/1/2019, 10:35:40 PM Β· Difficulty 11.2618 Β· 3,851,562 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ac362af2b71ae1754911a6a9867f79883a754efc7212e5d7befe70e91de1ad86
View on Chainz β†—

Difficulty

11.261837

Transactions

1

Size

200 B

Version

2

Bits

0b4307c6

Nonce

165,833,823

Timestamp

1/1/2019, 10:35:40 PM

Confirmations

3,851,562

Merkle Root

a45a3d5960aa354fb219c20c227603d1dbff269e0675928abd10e8f54dbc5535
Transactions (1)
Coinbasea45a3d5960aa35…10e8f54dbc5535
1 in β†’ 1 out7.8700 XPM110 B
AUhjokok…k5m93PZR
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.

6.688 Γ— 10⁹³(94-digit number)
66882466663598536437…18402176357925212000
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.688 Γ— 10⁹³(94-digit number)
66882466663598536437…18402176357925212001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.337 Γ— 10⁹⁴(95-digit number)
13376493332719707287…36804352715850424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.675 Γ— 10⁹⁴(95-digit number)
26752986665439414575…73608705431700848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.350 Γ— 10⁹⁴(95-digit number)
53505973330878829150…47217410863401696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.070 Γ— 10⁹⁡(96-digit number)
10701194666175765830…94434821726803392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.140 Γ— 10⁹⁡(96-digit number)
21402389332351531660…88869643453606784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.280 Γ— 10⁹⁡(96-digit number)
42804778664703063320…77739286907213568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.560 Γ— 10⁹⁡(96-digit number)
85609557329406126640…55478573814427136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.712 Γ— 10⁹⁢(97-digit number)
17121911465881225328…10957147628854272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.424 Γ— 10⁹⁢(97-digit number)
34243822931762450656…21914295257708544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.848 Γ— 10⁹⁢(97-digit number)
68487645863524901312…43828590515417088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.369 Γ— 10⁹⁷(98-digit number)
13697529172704980262…87657181030834176001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second 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
ExceptionalChain length 12
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2991556

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 ac362af2b71ae1754911a6a9867f79883a754efc7212e5d7befe70e91de1ad86

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 #2,991,556 on Chainz β†—
Circulating Supply:57,989,310 XPMΒ·at block #6,843,117 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