Block #298,012

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 12:54:09 AM · Difficulty 9.9919 · 6,492,928 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44689c65c784374a77f8d17d41ae9e197cdfabf063f6524f28f751606d97893b

View on Chainz ↗

Height

#298,012

Difficulty

9.991944

Transactions

Size

1.88 KB

Version

Bits

09fdf004

Nonce

254,472

Timestamp

12/7/2013, 12:54:09 AM

Confirmations

6,492,928

Merkle Root

6d7ae414ef6908bf4c6a0e9213b60be69d75fab8c83bb0bac82f77d44223a8e0

Transactions (5)

Coinbase423741b9108e30…bdc282e64f3344

1 in → 1 out10.0500 XPM110 B

AeKNrjNj…1NEq95Ta

aa5de728f6b7f0…ca5d91b3e6b5b4

5 in → 2 out26.0000 XPM818 B

AHuYt8e7…uPibQbBf AXgkPaw3…fsN6UcVQ

cc0370def35e4b…c5b61d15854b9b

1 in → 1 out10.0700 XPM157 B

AXfJYKVn…QktpQC8p

70a4ae8ab4c7fa…f2b5d6a47f32dd

3 in → 2 out119.4751 XPM524 B

AWHPfGRv…7QfH2BKk Ae3vUDij…TU7BEE7y

d3125f489d65af…186fa7b6674533

1 in → 2 out0.4800 XPM227 B

AVvyhacf…VgfUiyaR ARtCgrK2…6PgfAPf2

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.

1.263 × 10⁹⁶(97-digit number)

12635953693121378556…87818261749865881599

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

1.263 × 10⁹⁶(97-digit number)

12635953693121378556…87818261749865881599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.263 × 10⁹⁶(97-digit number)

12635953693121378556…87818261749865881601

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

2.527 × 10⁹⁶(97-digit number)

25271907386242757113…75636523499731763199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.527 × 10⁹⁶(97-digit number)

25271907386242757113…75636523499731763201

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

5.054 × 10⁹⁶(97-digit number)

50543814772485514227…51273046999463526399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.054 × 10⁹⁶(97-digit number)

50543814772485514227…51273046999463526401

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

1.010 × 10⁹⁷(98-digit number)

10108762954497102845…02546093998927052799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.010 × 10⁹⁷(98-digit number)

10108762954497102845…02546093998927052801

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

2.021 × 10⁹⁷(98-digit number)

20217525908994205691…05092187997854105599

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