Block #251,170

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 9:16:46 PM · Difficulty 9.9695 · 6,580,766 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4b1f1cace6597f3899da75a4632e433b8520cf7ced91ebffe47a99a076bfa73

View on Chainz ↗

Height

#251,170

Difficulty

9.969535

Transactions

Size

1.58 KB

Version

Bits

09f8336a

Nonce

24,075

Timestamp

11/8/2013, 9:16:46 PM

Confirmations

6,580,766

Mined by

⛏️ "aR}TAGbRhLj1HQi4pXYvW1G5HRrmefnZcEQFqQ

Merkle Root

40d4f3ff18b22dc7215af23d3d1bd26b7a992311b24613ec3e55a2eabef88431

Transactions (1)

Coinbase40d4f3ff18b22d…55a2eabef88431

1 in → 43 out10.0224 XPM1.49 KB

AGbRhLj1…nZcEQFqQ AYckRkCF…TgDe5VSp AeZuurfR…BADULmp6 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

7.613 × 10⁹⁴(95-digit number)

76133815971701559783…71951931972570514719

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

7.613 × 10⁹⁴(95-digit number)

76133815971701559783…71951931972570514719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.613 × 10⁹⁴(95-digit number)

76133815971701559783…71951931972570514721

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

1.522 × 10⁹⁵(96-digit number)

15226763194340311956…43903863945141029439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.522 × 10⁹⁵(96-digit number)

15226763194340311956…43903863945141029441

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

3.045 × 10⁹⁵(96-digit number)

30453526388680623913…87807727890282058879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.045 × 10⁹⁵(96-digit number)

30453526388680623913…87807727890282058881

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

6.090 × 10⁹⁵(96-digit number)

60907052777361247827…75615455780564117759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.090 × 10⁹⁵(96-digit number)

60907052777361247827…75615455780564117761

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

1.218 × 10⁹⁶(97-digit number)

12181410555472249565…51230911561128235519

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 #251,170

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