Block #2,644,179

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/2/2018, 9:27:43 AM · Difficulty 11.7039 · 4,188,630 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f71430275b481a84bd5005ec4e77ed6afc8b83bb47650197672b0b862a295ed

View on Chainz ↗

Height

#2,644,179

Difficulty

11.703874

Transactions

Size

992 B

Version

Bits

0bb4311a

Nonce

80,940,029

Timestamp

5/2/2018, 9:27:43 AM

Confirmations

4,188,630

Mined by

⛏️ P2SHASBDQ7zs4ntsHSAutoBFiWU51Vz3i2hb6h

Merkle Root

e935311ce93b2d8165a89bba19fd949fcd101185aa93a9cfcbaa6fa25e9206a4

Transactions (4)

Coinbase446bac2ad0c7c4…4909860aedf61b

1 in → 1 out7.3200 XPM110 B

ASBDQ7zs…z3i2hb6h

5408c489e039e3…d298b261b5cf47

1 in → 2 out7.4100 XPM193 B

ActzHSiQ…xAED36hQ AexMKjWh…arwxradq

5fee5f9efc614f…d246024232f364

2 in → 2 out4.7653 XPM373 B

APjAQiDf…D2v3t94v ANtJpY44…Mez5wyam

563a2608abb412…c014f809c4f4ed

1 in → 2 out1.2897 XPM226 B

ARJTFmXi…9mT6237k AZj7Sr6N…LA7fWs32

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.125 × 10⁹⁵(96-digit number)

21252031971222693578…17322677825058295999

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

2.125 × 10⁹⁵(96-digit number)

21252031971222693578…17322677825058295999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.125 × 10⁹⁵(96-digit number)

21252031971222693578…17322677825058296001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.250 × 10⁹⁵(96-digit number)

42504063942445387157…34645355650116591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.250 × 10⁹⁵(96-digit number)

42504063942445387157…34645355650116592001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.500 × 10⁹⁵(96-digit number)

85008127884890774314…69290711300233183999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.500 × 10⁹⁵(96-digit number)

85008127884890774314…69290711300233184001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.700 × 10⁹⁶(97-digit number)

17001625576978154862…38581422600466367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.700 × 10⁹⁶(97-digit number)

17001625576978154862…38581422600466368001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.400 × 10⁹⁶(97-digit number)

34003251153956309725…77162845200932735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.400 × 10⁹⁶(97-digit number)

34003251153956309725…77162845200932736001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.800 × 10⁹⁶(97-digit number)

68006502307912619451…54325690401865471999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,644,179

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