Block #34,365

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 6:24:28 AM · Difficulty 7.9932 · 6,755,418 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a391985bdbc75bc4ba28e8c3dc4e0186bc56b31bc7f7dd65fa43e0a230451f81

View on Chainz ↗

Height

#34,365

Difficulty

7.993193

Transactions

Size

662 B

Version

Bits

07fe41ed

Nonce

112

Timestamp

7/14/2013, 6:24:28 AM

Confirmations

6,755,418

Merkle Root

b27fb54884f569ea8fbefa3f7dc359ea72a6c8c3f6d57449ed45cf2d48ebbae0

Transactions (3)

Coinbasebffa7d4b21b2db…60bbc5c9191017

1 in → 1 out15.6500 XPM109 B

ATQXWTC8…KGpvr8ey

f40f39b47469d9…5babf881110853

2 in → 1 out19.5500 XPM305 B

AdhRYkdk…qwNrcYxb

06719f5d5e5664…4fd9248a1851eb

1 in → 1 out15.6400 XPM159 B

AXUtFnVB…2K4kmJnq

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.

1.341 × 10⁹³(94-digit number)

13417403076874201910…31791799510520972479

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

1.341 × 10⁹³(94-digit number)

13417403076874201910…31791799510520972479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.341 × 10⁹³(94-digit number)

13417403076874201910…31791799510520972481

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

2.683 × 10⁹³(94-digit number)

26834806153748403820…63583599021041944959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.683 × 10⁹³(94-digit number)

26834806153748403820…63583599021041944961

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

5.366 × 10⁹³(94-digit number)

53669612307496807641…27167198042083889919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.366 × 10⁹³(94-digit number)

53669612307496807641…27167198042083889921

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

1.073 × 10⁹⁴(95-digit number)

10733922461499361528…54334396084167779839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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