Block #2,646,428

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/3/2018, 8:49:00 AM · Difficulty 11.7498 · 4,194,451 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e89c63fa5d1e8d29788218dd18a6c46113b6a1c619bdf1148b8c79171732ef6

View on Chainz ↗

Height

#2,646,428

Difficulty

11.749803

Transactions

Size

1.59 KB

Version

Bits

0bbff314

Nonce

671,704,787

Timestamp

5/3/2018, 8:49:00 AM

Confirmations

4,194,451

Mined by

⛏️ P2SHAMPdFYPy265MJX7dTyZi4UNDGZfTWGuNaK

Merkle Root

326ab0932b069aaa46e3b62ffcd1df9684b6bdac7874f1e54683176e0c6fe7cb

Transactions (3)

Coinbase83e9bb69a79aac…6d8d9d6796829a

1 in → 1 out7.2600 XPM110 B

AMPdFYPy…fTWGuNaK

c280b62d4c309b…509fb0243b859d

9 in → 2 out52.1381 XPM1.18 KB

AGLtmPtU…6qEXYcoh AWp4iAg7…FUBLEm8x

6a4206748423cc…bd27e48435bce7

1 in → 2 out2.2586 XPM226 B

AHpTmk6K…TNVqNhJG Abn3ZzFV…7t3ZTAgc

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.

2.023 × 10⁹⁶(97-digit number)

20238671592248045086…01057994433816521919

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

2.023 × 10⁹⁶(97-digit number)

20238671592248045086…01057994433816521919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.023 × 10⁹⁶(97-digit number)

20238671592248045086…01057994433816521921

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

4.047 × 10⁹⁶(97-digit number)

40477343184496090173…02115988867633043839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.047 × 10⁹⁶(97-digit number)

40477343184496090173…02115988867633043841

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

8.095 × 10⁹⁶(97-digit number)

80954686368992180347…04231977735266087679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.095 × 10⁹⁶(97-digit number)

80954686368992180347…04231977735266087681

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

1.619 × 10⁹⁷(98-digit number)

16190937273798436069…08463955470532175359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.619 × 10⁹⁷(98-digit number)

16190937273798436069…08463955470532175361

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

3.238 × 10⁹⁷(98-digit number)

32381874547596872138…16927910941064350719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.238 × 10⁹⁷(98-digit number)

32381874547596872138…16927910941064350721

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

6.476 × 10⁹⁷(98-digit number)

64763749095193744277…33855821882128701439

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

6.476 × 10⁹⁷(98-digit number)

64763749095193744277…33855821882128701441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,646,428

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