Block #544,269

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2014, 7:27:17 PM · Difficulty 10.9501 · 6,269,771 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

69294cf9c3c76c6918e99edf48ef350101cc0100b1992d7a017184e9a333f364

View on Chainz ↗

Height

#544,269

Difficulty

10.950116

Transactions

Size

697 B

Version

Bits

0af33ad5

Nonce

38,104

Timestamp

5/14/2014, 7:27:17 PM

Confirmations

6,269,771

Mined by

⛏️ NaSsAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a75991b3567ee28dfdb730d3953f58e172fc1b67274c3f659c8fc48388722784

Transactions (1)

Coinbasea75991b3567ee2…8fc48388722784

1 in → 16 out8.3300 XPM607 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j

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.

5.912 × 10⁹⁵(96-digit number)

59121418866627349562…59351693777279731199

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

5.912 × 10⁹⁵(96-digit number)

59121418866627349562…59351693777279731199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.912 × 10⁹⁵(96-digit number)

59121418866627349562…59351693777279731201

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

1.182 × 10⁹⁶(97-digit number)

11824283773325469912…18703387554559462399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.182 × 10⁹⁶(97-digit number)

11824283773325469912…18703387554559462401

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

2.364 × 10⁹⁶(97-digit number)

23648567546650939824…37406775109118924799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.364 × 10⁹⁶(97-digit number)

23648567546650939824…37406775109118924801

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

4.729 × 10⁹⁶(97-digit number)

47297135093301879649…74813550218237849599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.729 × 10⁹⁶(97-digit number)

47297135093301879649…74813550218237849601

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

9.459 × 10⁹⁶(97-digit number)

94594270186603759299…49627100436475699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.459 × 10⁹⁶(97-digit number)

94594270186603759299…49627100436475699201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #544,269

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