XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,077,194

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/19/2017, 5:16:49 AM Β· Difficulty 10.8483 Β· 4,765,739 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
52094fabe45ecf9b647c0ceac892aa12d2731725c9a86d965b6f2df84c1eb4be
View on Chainz β†—

Height

#2,077,194

Difficulty

10.848331

Transactions

1

Size

201 B

Version

2

Bits

0ad92c39

Nonce

170,333,310

Timestamp

4/19/2017, 5:16:49 AM

Confirmations

4,765,739

Mined by

⛏️ P2SHAbwGcfRZj2NrxUo64eUX1NXntStu2W7ZaM

Merkle Root

8257d313ab7936518d0b65605e5e7c91d9d510ae9c9579586f9e02613f867fb4
Transactions (1)
Coinbase8257d313ab7936…9e02613f867fb4
1 in β†’ 1 out8.4800 XPM110 B
AbwGcfRZ…tu2W7ZaM
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.

1.623 Γ— 10⁹⁸(99-digit number)
16239912062170615210…31318459924025343999
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.623 Γ— 10⁹⁸(99-digit number)
16239912062170615210…31318459924025343999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.623 Γ— 10⁹⁸(99-digit number)
16239912062170615210…31318459924025344001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.247 Γ— 10⁹⁸(99-digit number)
32479824124341230420…62636919848050687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.247 Γ— 10⁹⁸(99-digit number)
32479824124341230420…62636919848050688001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
6.495 Γ— 10⁹⁸(99-digit number)
64959648248682460841…25273839696101375999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.495 Γ— 10⁹⁸(99-digit number)
64959648248682460841…25273839696101376001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁹(100-digit number)
12991929649736492168…50547679392202751999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.299 Γ— 10⁹⁹(100-digit number)
12991929649736492168…50547679392202752001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.598 Γ— 10⁹⁹(100-digit number)
25983859299472984336…01095358784405503999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.598 Γ— 10⁹⁹(100-digit number)
25983859299472984336…01095358784405504001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,987,813 XPMΒ·at block #6,842,932 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