Block #481,587

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 11:47:12 PM · Difficulty 10.5343 · 6,334,808 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fe1ac4ef64e58f4ffacf031542c8f1a29f11122549a9243f45a7d3fafbd45c5

View on Chainz ↗

Height

#481,587

Difficulty

10.534317

Transactions

Size

1003 B

Version

Bits

0a88c900

Nonce

403,687

Timestamp

4/8/2014, 11:47:12 PM

Confirmations

6,334,808

Mined by

⛏️ 3YaSDxAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

de691aefaf73c6f35d59390836df5787e288b4063226d6568285c3547b7ae3f4

Transactions (1)

Coinbasede691aefaf73c6…85c3547b7ae3f4

1 in → 25 out9.0000 XPM913 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR

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.

2.136 × 10⁹⁴(95-digit number)

21364296520392048741…07595364007968959999

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

2.136 × 10⁹⁴(95-digit number)

21364296520392048741…07595364007968959999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.136 × 10⁹⁴(95-digit number)

21364296520392048741…07595364007968960001

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

4.272 × 10⁹⁴(95-digit number)

42728593040784097483…15190728015937919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.272 × 10⁹⁴(95-digit number)

42728593040784097483…15190728015937920001

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

8.545 × 10⁹⁴(95-digit number)

85457186081568194967…30381456031875839999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.545 × 10⁹⁴(95-digit number)

85457186081568194967…30381456031875840001

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

1.709 × 10⁹⁵(96-digit number)

17091437216313638993…60762912063751679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.709 × 10⁹⁵(96-digit number)

17091437216313638993…60762912063751680001

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

3.418 × 10⁹⁵(96-digit number)

34182874432627277986…21525824127503359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.418 × 10⁹⁵(96-digit number)

34182874432627277986…21525824127503360001

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 #481,587

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