Block #307,345

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 12:41:17 PM · Difficulty 9.9942 · 6,498,958 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46c6a5ae29055f0cacf30bb7523c7d943e08c010aafa7601983c69a81f5621fe

View on Chainz ↗

Height

#307,345

Difficulty

9.994183

Transactions

Size

1.14 KB

Version

Bits

09fe82c3

Nonce

4,532

Timestamp

12/12/2013, 12:41:17 PM

Confirmations

6,498,958

Mined by

⛏️ aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

4d0a296ce0d0b65903c0078073d21f060ab0d5f353bdcee54ab2b182526cd911

Transactions (1)

Coinbase4d0a296ce0d0b6…b2b182526cd911

1 in → 30 out9.9800 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz AZ2pPuKg…95SN2Yr7 AdwTEXyC…NwbVbqZV AMbCuLHZ…WSoStwkc AQDGVS66…1PTWdWkm

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.

2.369 × 10⁹³(94-digit number)

23691720645672853593…03521534121869823999

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

2.369 × 10⁹³(94-digit number)

23691720645672853593…03521534121869823999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.369 × 10⁹³(94-digit number)

23691720645672853593…03521534121869824001

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

4.738 × 10⁹³(94-digit number)

47383441291345707187…07043068243739647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.738 × 10⁹³(94-digit number)

47383441291345707187…07043068243739648001

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

9.476 × 10⁹³(94-digit number)

94766882582691414374…14086136487479295999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.476 × 10⁹³(94-digit number)

94766882582691414374…14086136487479296001

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

1.895 × 10⁹⁴(95-digit number)

18953376516538282874…28172272974958591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.895 × 10⁹⁴(95-digit number)

18953376516538282874…28172272974958592001

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

3.790 × 10⁹⁴(95-digit number)

37906753033076565749…56344545949917183999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.790 × 10⁹⁴(95-digit number)

37906753033076565749…56344545949917184001

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 #307,345

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