XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,641,129

Block #2,641,129

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 6:08:03 AM Β· Difficulty 11.6081 Β· 4,202,184 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
483d89788c1576f0f4c45e4a4dcb523d9ff4d23a31d27e4840194f3a6559f3c7
View on Chainz β†—

Difficulty

11.608144

Transactions

1

Size

200 B

Version

2

Bits

0b9baf57

Nonce

152,931,971

Timestamp

5/1/2018, 6:08:03 AM

Confirmations

4,202,184

Merkle Root

dbdb0abfad04054a1a73fc1999e8ef9238292646733afb147bcb025e4a4cda91
Transactions (1)
Coinbasedbdb0abfad0405…cb025e4a4cda91
1 in β†’ 1 out7.4100 XPM110 B
AYMAX47o…4F6mV1cU
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.

1.720 Γ— 10⁹⁡(96-digit number)
17207508374120188086…05332448705772631300
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
1.720 Γ— 10⁹⁡(96-digit number)
17207508374120188086…05332448705772631301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.441 Γ— 10⁹⁡(96-digit number)
34415016748240376172…10664897411545262601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.883 Γ— 10⁹⁡(96-digit number)
68830033496480752345…21329794823090525201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.376 Γ— 10⁹⁢(97-digit number)
13766006699296150469…42659589646181050401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.753 Γ— 10⁹⁢(97-digit number)
27532013398592300938…85319179292362100801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.506 Γ— 10⁹⁢(97-digit number)
55064026797184601876…70638358584724201601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.101 Γ— 10⁹⁷(98-digit number)
11012805359436920375…41276717169448403201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.202 Γ— 10⁹⁷(98-digit number)
22025610718873840750…82553434338896806401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.405 Γ— 10⁹⁷(98-digit number)
44051221437747681501…65106868677793612801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.810 Γ— 10⁹⁷(98-digit number)
88102442875495363002…30213737355587225601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.762 Γ— 10⁹⁸(99-digit number)
17620488575099072600…60427474711174451201
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 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
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 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 2641129

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 483d89788c1576f0f4c45e4a4dcb523d9ff4d23a31d27e4840194f3a6559f3c7

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 #2,641,129 on Chainz β†—
Circulating Supply:57,990,862 XPMΒ·at block #6,843,312 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