Block #483,985

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 8:15:40 AM · Difficulty 10.5750 · 6,315,385 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75436b3bb570206ac938e814514b48f360ae0f6e1bacbb4816dfe23a3c717cec

View on Chainz ↗

Height

#483,985

Difficulty

10.575036

Transactions

Size

1.02 KB

Version

Bits

0a93358e

Nonce

365,462,614

Timestamp

4/10/2014, 8:15:40 AM

Confirmations

6,315,385

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c1d2a5eee25248dbc16f6831bfcf1b66962aeb0d6f728f891c5522c1d6a3ea49

Transactions (2)

Coinbasee396fb31c8677f…46ed087543b351

1 in → 1 out8.9400 XPM116 B

AbwWkWZt…kawDhufa

cacf72feb8426c…87c260838003bc

4 in → 11 out36.1700 XPM840 B

AYH3TsEE…z8QwfCk6 APaJvQ3G…25PSkPEZ AZwXBq4j…rzStTzBk AVrzMBgN…EVKZMzxb ALrZxq5u…jReX3z9e

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.

5.499 × 10⁹⁹(100-digit number)

54991195418274100308…22482128350281748479

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

5.499 × 10⁹⁹(100-digit number)

54991195418274100308…22482128350281748479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.499 × 10⁹⁹(100-digit number)

54991195418274100308…22482128350281748481

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

1.099 × 10¹⁰⁰(101-digit number)

10998239083654820061…44964256700563496959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.099 × 10¹⁰⁰(101-digit number)

10998239083654820061…44964256700563496961

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

2.199 × 10¹⁰⁰(101-digit number)

21996478167309640123…89928513401126993919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.199 × 10¹⁰⁰(101-digit number)

21996478167309640123…89928513401126993921

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

4.399 × 10¹⁰⁰(101-digit number)

43992956334619280246…79857026802253987839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.399 × 10¹⁰⁰(101-digit number)

43992956334619280246…79857026802253987841

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

8.798 × 10¹⁰⁰(101-digit number)

87985912669238560493…59714053604507975679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.798 × 10¹⁰⁰(101-digit number)

87985912669238560493…59714053604507975681

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