Block #305,247

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 9:23:29 AM · Difficulty 9.9935 · 6,502,498 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3eb9ad024580f3a0d129bb3de5345627784d0f5b4db43863aede248b1a84d817

View on Chainz ↗

Height

#305,247

Difficulty

9.993540

Transactions

Size

1.18 KB

Version

Bits

09fe589d

Nonce

231,458

Timestamp

12/11/2013, 9:23:29 AM

Confirmations

6,502,498

Mined by

⛏️ _aR.APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

3c624664208fd0361696b9cfed17ac89c9a3ea8753059043e199f4cb2465ef95

Transactions (1)

Coinbase3c624664208fd0…99f4cb2465ef95

1 in → 31 out9.9800 XPM1.09 KB

APeshfYV…3PKcKMKH ATiP2myP…qVUH8Grb AKwqFUdz…D4jGNKFN Ae7UyoY4…DtgAv9cY AQyr8Lw3…hs4nt3Pn

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.

2.103 × 10⁹⁵(96-digit number)

21032202197383320366…95990257083681550719

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

2.103 × 10⁹⁵(96-digit number)

21032202197383320366…95990257083681550719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.103 × 10⁹⁵(96-digit number)

21032202197383320366…95990257083681550721

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

4.206 × 10⁹⁵(96-digit number)

42064404394766640732…91980514167363101439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.206 × 10⁹⁵(96-digit number)

42064404394766640732…91980514167363101441

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

8.412 × 10⁹⁵(96-digit number)

84128808789533281465…83961028334726202879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.412 × 10⁹⁵(96-digit number)

84128808789533281465…83961028334726202881

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

1.682 × 10⁹⁶(97-digit number)

16825761757906656293…67922056669452405759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.682 × 10⁹⁶(97-digit number)

16825761757906656293…67922056669452405761

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

3.365 × 10⁹⁶(97-digit number)

33651523515813312586…35844113338904811519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.365 × 10⁹⁶(97-digit number)

33651523515813312586…35844113338904811521

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 #305,247

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