Block #34,475

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 6:33:57 AM · Difficulty 7.9933 · 6,792,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

15434d7dfc9e596f8fc7978bf6b41cc104e96503442443db3fb4540ed71e88c5

View on Chainz ↗

Height

#34,475

Difficulty

7.993331

Transactions

Size

198 B

Version

Bits

07fe4af2

Nonce

340

Timestamp

7/14/2013, 6:33:57 AM

Confirmations

6,792,651

Mined by

⛏️ P2SHAHdhnVHaW7jLXPLghE5UqKnnmaxHqEjaxD

Merkle Root

c9537f1b1197d046301df5311d1dfbb64c376b7c45e9cb446b2f6c8cec78c382

Transactions (1)

Coinbasec9537f1b1197d0…2f6c8cec78c382

1 in → 1 out15.6300 XPM110 B

AHdhnVHa…xHqEjaxD

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.

6.292 × 10⁸⁸(89-digit number)

62923111712669183139…64885739008105428599

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

6.292 × 10⁸⁸(89-digit number)

62923111712669183139…64885739008105428599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.292 × 10⁸⁸(89-digit number)

62923111712669183139…64885739008105428601

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

1.258 × 10⁸⁹(90-digit number)

12584622342533836627…29771478016210857199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.258 × 10⁸⁹(90-digit number)

12584622342533836627…29771478016210857201

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

2.516 × 10⁸⁹(90-digit number)

25169244685067673255…59542956032421714399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.516 × 10⁸⁹(90-digit number)

25169244685067673255…59542956032421714401

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

5.033 × 10⁸⁹(90-digit number)

50338489370135346511…19085912064843428799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.033 × 10⁸⁹(90-digit number)

50338489370135346511…19085912064843428801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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

Block #34,475

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