Block #2,646,178

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 5:56:07 AM · Difficulty 11.7459 · 4,184,939 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96166c36fa66813b861f4bc7b68312102268587e71b874dd3b2ab4a62bbfcbc5

View on Chainz ↗

Height

#2,646,178

Difficulty

11.745911

Transactions

Size

872 B

Version

Bits

0bbef403

Nonce

152,553,028

Timestamp

5/3/2018, 5:56:07 AM

Confirmations

4,184,939

Mined by

⛏️ P2SHAbioJneRaYSFab4MkEeHrBQ3u7xG3yspQQ

Merkle Root

00b567c1aa17b9e6f4bdb87426eb40e548c937cfb0c1109bad22c033bcf14f26

Transactions (2)

Coinbase37328e5b5da62f…f9eca2b47bb62d

1 in → 1 out7.2500 XPM110 B

AbioJneR…xG3yspQQ

940c28b631872f…d29f34af4e0be6

4 in → 2 out867.7463 XPM671 B

AenurARz…nKuCAFnD AY6hDknN…jLU3Mpky

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.

4.301 × 10⁹⁶(97-digit number)

43018060788366113666…32913659624420638719

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

4.301 × 10⁹⁶(97-digit number)

43018060788366113666…32913659624420638719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.301 × 10⁹⁶(97-digit number)

43018060788366113666…32913659624420638721

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

8.603 × 10⁹⁶(97-digit number)

86036121576732227332…65827319248841277439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.603 × 10⁹⁶(97-digit number)

86036121576732227332…65827319248841277441

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

1.720 × 10⁹⁷(98-digit number)

17207224315346445466…31654638497682554879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.720 × 10⁹⁷(98-digit number)

17207224315346445466…31654638497682554881

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

3.441 × 10⁹⁷(98-digit number)

34414448630692890932…63309276995365109759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.441 × 10⁹⁷(98-digit number)

34414448630692890932…63309276995365109761

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

6.882 × 10⁹⁷(98-digit number)

68828897261385781865…26618553990730219519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.882 × 10⁹⁷(98-digit number)

68828897261385781865…26618553990730219521

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

1.376 × 10⁹⁸(99-digit number)

13765779452277156373…53237107981460439039

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 #2,646,178

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