Block #43,255

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 8:33:33 PM · Difficulty 8.6527 · 6,752,432 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36c7dc2fe5f1bb9fa03ac97348c94c1291b025e6404cea9efefe38dbf134b042

View on Chainz ↗

Height

#43,255

Difficulty

8.652745

Transactions

Size

199 B

Version

Bits

08a71a49

Nonce

Timestamp

7/14/2013, 8:33:33 PM

Confirmations

6,752,432

Mined by

⛏️ P2SHAV3JuPMPrXbiQfyA8ZqDGV3T9qouBnijyH

Merkle Root

37ac38030a7a133de5abbd5f11afdcfe60dac3f14a87706877d49e10f2504a4f

Transactions (1)

Coinbase37ac38030a7a13…d49e10f2504a4f

1 in → 1 out13.3400 XPM110 B

AV3JuPMP…ouBnijyH

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.

4.959 × 10⁹¹(92-digit number)

49596091227286421630…24963636237182996999

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

4.959 × 10⁹¹(92-digit number)

49596091227286421630…24963636237182996999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.959 × 10⁹¹(92-digit number)

49596091227286421630…24963636237182997001

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

9.919 × 10⁹¹(92-digit number)

99192182454572843261…49927272474365993999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.919 × 10⁹¹(92-digit number)

99192182454572843261…49927272474365994001

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

1.983 × 10⁹²(93-digit number)

19838436490914568652…99854544948731987999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.983 × 10⁹²(93-digit number)

19838436490914568652…99854544948731988001

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

3.967 × 10⁹²(93-digit number)

39676872981829137304…99709089897463975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.967 × 10⁹²(93-digit number)

39676872981829137304…99709089897463976001

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