Block #273,427

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 7:21:11 PM · Difficulty 9.9548 · 6,533,015 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

227a0d4c6c027aee7ce955d3c846e554e0dfcef2f6a6c7a610b5aacae8f36059

View on Chainz ↗

Height

#273,427

Difficulty

9.954820

Transactions

Size

1.21 KB

Version

Bits

09f46f13

Nonce

49,739

Timestamp

11/25/2013, 7:21:11 PM

Confirmations

6,533,015

Mined by

⛏️ ,aR!@Ab3J4ipopCDiBmuX9CWCummQr4GaHrWuuW

Merkle Root

dfc44c4f9a5edd63f4885b30d8807faef03d6caf4468386e8984978a8bdd3e68

Transactions (1)

Coinbasedfc44c4f9a5edd…84978a8bdd3e68

1 in → 32 out10.0600 XPM1.12 KB

Ab3J4ipo…GaHrWuuW AQyr8Lw3…hs4nt3Pn ANQKf2g4…29NaVj23 AJ583KJv…3M16nmdw AMBbmvEz…yFqmSmw2

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.

7.998 × 10⁹³(94-digit number)

79982199722342261545…37270571522837332479

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

7.998 × 10⁹³(94-digit number)

79982199722342261545…37270571522837332479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.998 × 10⁹³(94-digit number)

79982199722342261545…37270571522837332481

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

1.599 × 10⁹⁴(95-digit number)

15996439944468452309…74541143045674664959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.599 × 10⁹⁴(95-digit number)

15996439944468452309…74541143045674664961

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

3.199 × 10⁹⁴(95-digit number)

31992879888936904618…49082286091349329919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.199 × 10⁹⁴(95-digit number)

31992879888936904618…49082286091349329921

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

6.398 × 10⁹⁴(95-digit number)

63985759777873809236…98164572182698659839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.398 × 10⁹⁴(95-digit number)

63985759777873809236…98164572182698659841

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

1.279 × 10⁹⁵(96-digit number)

12797151955574761847…96329144365397319679

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 #273,427

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