Block #215,977

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 11:22:53 AM · Difficulty 9.9253 · 6,593,330 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49ed6c3a176f3ed369447886f2a61f53b4f3241e6cf24ca12c3fe6dea3568495

View on Chainz ↗

Height

#215,977

Difficulty

9.925314

Transactions

Size

390 B

Version

Bits

09ece165

Nonce

203,708

Timestamp

10/18/2013, 11:22:53 AM

Confirmations

6,593,330

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

35d179e13515987a43e9cfa4a82e56926aa2025174e8a1b03e47a766d8969a19

Transactions (2)

Coinbase1190db104d59fd…008e4cc6b60d11

1 in → 1 out10.1500 XPM110 B

AbuU1HhS…JPwsJEbB

8f0a7e9bcf64a9…f60b0ecd91a341

1 in → 2 out10.1400 XPM191 B

AQAvQSWZ…C9mFkvux AcsixBRe…rdAAPHsQ

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.

1.026 × 10⁹³(94-digit number)

10267144004280437105…20135864052085363839

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

1.026 × 10⁹³(94-digit number)

10267144004280437105…20135864052085363839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.026 × 10⁹³(94-digit number)

10267144004280437105…20135864052085363841

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

2.053 × 10⁹³(94-digit number)

20534288008560874210…40271728104170727679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.053 × 10⁹³(94-digit number)

20534288008560874210…40271728104170727681

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

4.106 × 10⁹³(94-digit number)

41068576017121748420…80543456208341455359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.106 × 10⁹³(94-digit number)

41068576017121748420…80543456208341455361

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

8.213 × 10⁹³(94-digit number)

82137152034243496840…61086912416682910719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.213 × 10⁹³(94-digit number)

82137152034243496840…61086912416682910721

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

1.642 × 10⁹⁴(95-digit number)

16427430406848699368…22173824833365821439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #215,977

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