Block #306,884

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 7:30:06 AM · Difficulty 9.9940 · 6,510,256 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

025b85aff955f4f2c4126c56b19fb7ca217deb0e77459fe1c13bae8d17b43c2a

View on Chainz ↗

Height

#306,884

Difficulty

9.993993

Transactions

Size

213 B

Version

Bits

09fe7650

Nonce

516

Timestamp

12/12/2013, 7:30:06 AM

Confirmations

6,510,256

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f01097c2f1460508529d126fc44e8c06ce6b8d29324cacf8c00997fa6044a4fa

Transactions (1)

Coinbasef01097c2f14605…0997fa6044a4fa

1 in → 1 out10.0000 XPM116 B

AbwWkWZt…kawDhufa

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.

2.379 × 10¹¹²(113-digit number)

23790678785501213024…18225742568911831039

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

2.379 × 10¹¹²(113-digit number)

23790678785501213024…18225742568911831039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.379 × 10¹¹²(113-digit number)

23790678785501213024…18225742568911831041

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

4.758 × 10¹¹²(113-digit number)

47581357571002426049…36451485137823662079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.758 × 10¹¹²(113-digit number)

47581357571002426049…36451485137823662081

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

9.516 × 10¹¹²(113-digit number)

95162715142004852099…72902970275647324159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.516 × 10¹¹²(113-digit number)

95162715142004852099…72902970275647324161

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

1.903 × 10¹¹³(114-digit number)

19032543028400970419…45805940551294648319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.903 × 10¹¹³(114-digit number)

19032543028400970419…45805940551294648321

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

3.806 × 10¹¹³(114-digit number)

38065086056801940839…91611881102589296639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.806 × 10¹¹³(114-digit number)

38065086056801940839…91611881102589296641

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 #306,884

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