Block #272,518

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 7:23:49 AM · Difficulty 9.9530 · 6,536,159 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

730992ba386af73c07e4b63bc75c426608bb545d6095f12f4112a4b13da4386b

View on Chainz ↗

Height

#272,518

Difficulty

9.953036

Transactions

Size

1.15 KB

Version

Bits

09f3fa2b

Nonce

65,384

Timestamp

11/25/2013, 7:23:49 AM

Confirmations

6,536,159

Mined by

⛏️ aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

122db21b18ce21111fba787674b8639ab5fd2e1b2319cbe7e2174f6458edef2f

Transactions (1)

Coinbase122db21b18ce21…174f6458edef2f

1 in → 30 out10.0600 XPM1.06 KB

APeshfYV…3PKcKMKH Aai6TNLM…kQf2QbQd AaSot6r4…DjoWHEUX AQyr8Lw3…hs4nt3Pn 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.

4.602 × 10⁹³(94-digit number)

46024393411100623702…31835959106341670399

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

4.602 × 10⁹³(94-digit number)

46024393411100623702…31835959106341670399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.602 × 10⁹³(94-digit number)

46024393411100623702…31835959106341670401

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

9.204 × 10⁹³(94-digit number)

92048786822201247405…63671918212683340799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.204 × 10⁹³(94-digit number)

92048786822201247405…63671918212683340801

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

1.840 × 10⁹⁴(95-digit number)

18409757364440249481…27343836425366681599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.840 × 10⁹⁴(95-digit number)

18409757364440249481…27343836425366681601

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

3.681 × 10⁹⁴(95-digit number)

36819514728880498962…54687672850733363199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.681 × 10⁹⁴(95-digit number)

36819514728880498962…54687672850733363201

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

7.363 × 10⁹⁴(95-digit number)

73639029457760997924…09375345701466726399

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 #272,518

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