Block #298,076

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 2:04:59 AM · Difficulty 9.9919 · 6,504,629 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46414823dc0e9c5551e831fe564da33d79c98f0ba99f94487487b05de06cf2c9

View on Chainz ↗

Height

#298,076

Difficulty

9.991932

Transactions

Size

1.18 KB

Version

Bits

09fdef3c

Nonce

143,672

Timestamp

12/7/2013, 2:04:59 AM

Confirmations

6,504,629

Mined by

⛏️ \aR>APvpz12Ne3y3GdSQX5xb8QzBwoNjdsxTYA

Merkle Root

7a40998f24e2f3e70969afd6b8f093a07bf07b89f2a0c399792f178035dc2fd0

Transactions (1)

Coinbase7a40998f24e2f3…2f178035dc2fd0

1 in → 31 out9.9789 XPM1.09 KB

APvpz12N…NjdsxTYA ASXEwJrb…E3MLWChF AN8nUzff…YcDfRDQ2 AcC2zSod…rtWatH79 AGXewNDY…FgKQN3gK

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.

1.197 × 10⁹⁷(98-digit number)

11975054198361168724…12161730196714241099

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

1.197 × 10⁹⁷(98-digit number)

11975054198361168724…12161730196714241099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.197 × 10⁹⁷(98-digit number)

11975054198361168724…12161730196714241101

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

2.395 × 10⁹⁷(98-digit number)

23950108396722337448…24323460393428482199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.395 × 10⁹⁷(98-digit number)

23950108396722337448…24323460393428482201

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

4.790 × 10⁹⁷(98-digit number)

47900216793444674896…48646920786856964399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.790 × 10⁹⁷(98-digit number)

47900216793444674896…48646920786856964401

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

9.580 × 10⁹⁷(98-digit number)

95800433586889349793…97293841573713928799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.580 × 10⁹⁷(98-digit number)

95800433586889349793…97293841573713928801

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

1.916 × 10⁹⁸(99-digit number)

19160086717377869958…94587683147427857599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.916 × 10⁹⁸(99-digit number)

19160086717377869958…94587683147427857601

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