Block #144,969

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/1/2013, 3:19:03 PM · Difficulty 9.8414 · 6,658,589 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

beeb0c3ae54e75c2fffb1ae92c1bd66f72514888e1d88731ec05f55b1e8c94b5

View on Chainz ↗

Height

#144,969

Difficulty

9.841416

Transactions

Size

198 B

Version

Bits

09d76711

Nonce

32,766

Timestamp

9/1/2013, 3:19:03 PM

Confirmations

6,658,589

Mined by

⛏️ P2SHAXGnUfJZw7g3fwFVGKyN2GLpoiBVGAtVkB

Merkle Root

819f8fef923c008a9cf940cbf081510d1f21e56119f0ddf3ded07412e125930a

Transactions (1)

Coinbase819f8fef923c00…d07412e125930a

1 in → 1 out10.3100 XPM109 B

AXGnUfJZ…BVGAtVkB

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.

1.536 × 10⁹²(93-digit number)

15361940221165173456…28437973705392486399

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

1.536 × 10⁹²(93-digit number)

15361940221165173456…28437973705392486399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.536 × 10⁹²(93-digit number)

15361940221165173456…28437973705392486401

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

3.072 × 10⁹²(93-digit number)

30723880442330346912…56875947410784972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.072 × 10⁹²(93-digit number)

30723880442330346912…56875947410784972801

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

6.144 × 10⁹²(93-digit number)

61447760884660693824…13751894821569945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.144 × 10⁹²(93-digit number)

61447760884660693824…13751894821569945601

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

1.228 × 10⁹³(94-digit number)

12289552176932138764…27503789643139891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.228 × 10⁹³(94-digit number)

12289552176932138764…27503789643139891201

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

2.457 × 10⁹³(94-digit number)

24579104353864277529…55007579286279782399

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