Block #304,215

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 7:31:46 PM · Difficulty 9.9933 · 6,502,857 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

34d7bf46a3126cb6a5fefacdc19afb2fba914b812e802935f6002efcb2a0c443

View on Chainz ↗

Height

#304,215

Difficulty

9.993262

Transactions

Size

1.78 KB

Version

Bits

09fe466a

Nonce

234,842

Timestamp

12/10/2013, 7:31:46 PM

Confirmations

6,502,857

Mined by

⛏️ WaRkAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

a4cf17a3546b60a7a003ea2f813cc81467067c53157e4d16dc2094464cced37e

Transactions (4)

Coinbase92e85949b990e0…1f9866112c9349

1 in → 29 out9.9800 XPM1.02 KB

AYtDvcGs…VuAcA7m7 AG5YAjec…VhA4Aeh1 AJzWx2VD…j4ZSMit5 AMdvB6BS…DPq9FYdA ALAFH3kk…VBdunEdz

a2f0c70966eae1…7b8175757e9d8e

1 in → 2 out1.9111 XPM227 B

AVWj3J2F…s8P6MeF8 ASUt5A7g…6CSmtegs

de6ddb0cf3aa97…7ce510fd16966f

1 in → 2 out1.4153 XPM226 B

AMtmbGHt…fG3q3p9L APcVt1yi…HhpCMe9P

6b5cb7fa1d2956…c8e13034d8549b

1 in → 2 out1.3654 XPM226 B

ANuqZCke…M5abw22A AaW9uUGi…F3fvgxNH

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.

1.386 × 10⁹⁶(97-digit number)

13864048969842585149…62726136013215246399

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

1.386 × 10⁹⁶(97-digit number)

13864048969842585149…62726136013215246399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.386 × 10⁹⁶(97-digit number)

13864048969842585149…62726136013215246401

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

2.772 × 10⁹⁶(97-digit number)

27728097939685170298…25452272026430492799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.772 × 10⁹⁶(97-digit number)

27728097939685170298…25452272026430492801

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

5.545 × 10⁹⁶(97-digit number)

55456195879370340597…50904544052860985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.545 × 10⁹⁶(97-digit number)

55456195879370340597…50904544052860985601

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

1.109 × 10⁹⁷(98-digit number)

11091239175874068119…01809088105721971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.109 × 10⁹⁷(98-digit number)

11091239175874068119…01809088105721971201

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

2.218 × 10⁹⁷(98-digit number)

22182478351748136239…03618176211443942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.218 × 10⁹⁷(98-digit number)

22182478351748136239…03618176211443942401

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 #304,215

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