Block #145,731

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/2/2013, 2:06:31 AM · Difficulty 9.8450 · 6,645,410 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

03d11ff1b7ad4924963e780d6b4b59dfffefb3053693945b61d0380829260ac0

View on Chainz ↗

Height

#145,731

Difficulty

9.844994

Transactions

Size

198 B

Version

Bits

09d85180

Nonce

34,217

Timestamp

9/2/2013, 2:06:31 AM

Confirmations

6,645,410

Merkle Root

4b1d6852bb1504413731c22bc50cf882cfc703c01797446e8539ee5dda7a2cd7

Transactions (1)

Coinbase4b1d6852bb1504…39ee5dda7a2cd7

1 in → 1 out10.3000 XPM109 B

AWbm4AWf…zNGrUw91

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.

1.844 × 10⁹¹(92-digit number)

18442318767350800152…27646787826896503879

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

1.844 × 10⁹¹(92-digit number)

18442318767350800152…27646787826896503879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.844 × 10⁹¹(92-digit number)

18442318767350800152…27646787826896503881

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

3.688 × 10⁹¹(92-digit number)

36884637534701600305…55293575653793007759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.688 × 10⁹¹(92-digit number)

36884637534701600305…55293575653793007761

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

7.376 × 10⁹¹(92-digit number)

73769275069403200610…10587151307586015519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.376 × 10⁹¹(92-digit number)

73769275069403200610…10587151307586015521

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

1.475 × 10⁹²(93-digit number)

14753855013880640122…21174302615172031039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.475 × 10⁹²(93-digit number)

14753855013880640122…21174302615172031041

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

2.950 × 10⁹²(93-digit number)

29507710027761280244…42348605230344062079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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