Block #287,524

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 8:49:01 AM · Difficulty 9.9868 · 6,506,839 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2adef19598440f7b4c227ffc76c3ce82772f94f6139a0cb7cb1574930bed4fd6

View on Chainz ↗

Height

#287,524

Difficulty

9.986761

Transactions

Size

1.18 KB

Version

Bits

09fc9c64

Nonce

19,360

Timestamp

12/1/2013, 8:49:01 AM

Confirmations

6,506,839

Merkle Root

018f14b12855acb28e81598b921ee9aef5f460ac775adc70e034b83e0d27fab5

Transactions (1)

Coinbase018f14b12855ac…34b83e0d27fab5

1 in → 31 out9.9900 XPM1.09 KB

AZ2pPuKg…95SN2Yr7 AN63YyQR…1tfe566A Acs9SHrk…QJSB8SFG Ae58nAEb…GFUA15fv AQ7ar5wG…hBCAeEwD

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.

9.809 × 10⁹⁸(99-digit number)

98099843859521658422…31848876555006907839

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

9.809 × 10⁹⁸(99-digit number)

98099843859521658422…31848876555006907839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.809 × 10⁹⁸(99-digit number)

98099843859521658422…31848876555006907841

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

1.961 × 10⁹⁹(100-digit number)

19619968771904331684…63697753110013815679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.961 × 10⁹⁹(100-digit number)

19619968771904331684…63697753110013815681

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

3.923 × 10⁹⁹(100-digit number)

39239937543808663369…27395506220027631359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.923 × 10⁹⁹(100-digit number)

39239937543808663369…27395506220027631361

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

7.847 × 10⁹⁹(100-digit number)

78479875087617326738…54791012440055262719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.847 × 10⁹⁹(100-digit number)

78479875087617326738…54791012440055262721

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

1.569 × 10¹⁰⁰(101-digit number)

15695975017523465347…09582024880110525439

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