Block #483,587

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 3:27:06 AM · Difficulty 10.5655 · 6,347,960 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

756187568571f33263d84c8efa903e75e74d371d2a9bf4f0074cdf8e74767eba

View on Chainz ↗

Height

#483,587

Difficulty

10.565538

Transactions

Size

575 B

Version

Bits

0a90c715

Nonce

353,242

Timestamp

4/10/2014, 3:27:06 AM

Confirmations

6,347,960

Mined by

⛏️ P2SHAM6vSPVLaMKYKcktRZu6qw5e68VdXNbD9Q

Merkle Root

3b5f3f7031c2972ef5f33da52404861b5a8694c4d14b118e49954b2f1820a4d4

Transactions (2)

Coinbasec6c8c87efdcab1…06de3f8a706502

1 in → 1 out8.9500 XPM109 B

AM6vSPVL…VdXNbD9Q

8022931640e43b…0c82db12e9040e

2 in → 2 out3.0173 XPM374 B

ALBrG2SM…xQfGoc8x AeGGwMwe…RqevLn5R

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.

5.239 × 10⁹⁸(99-digit number)

52399819646329550990…29975422775662673919

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

5.239 × 10⁹⁸(99-digit number)

52399819646329550990…29975422775662673919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.239 × 10⁹⁸(99-digit number)

52399819646329550990…29975422775662673921

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

1.047 × 10⁹⁹(100-digit number)

10479963929265910198…59950845551325347839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.047 × 10⁹⁹(100-digit number)

10479963929265910198…59950845551325347841

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

2.095 × 10⁹⁹(100-digit number)

20959927858531820396…19901691102650695679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.095 × 10⁹⁹(100-digit number)

20959927858531820396…19901691102650695681

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

4.191 × 10⁹⁹(100-digit number)

41919855717063640792…39803382205301391359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.191 × 10⁹⁹(100-digit number)

41919855717063640792…39803382205301391361

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

8.383 × 10⁹⁹(100-digit number)

83839711434127281585…79606764410602782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.383 × 10⁹⁹(100-digit number)

83839711434127281585…79606764410602782721

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 #483,587

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