Block #143,954

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/1/2013, 12:49:58 AM · Difficulty 9.8367 · 6,651,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

63890355b8eb792b38819c081dcdbec5332a170738131c33876a9b3b47e396ec

View on Chainz ↗

Height

#143,954

Difficulty

9.836728

Transactions

Size

356 B

Version

Bits

09d633d3

Nonce

16,363

Timestamp

9/1/2013, 12:49:58 AM

Confirmations

6,651,511

Mined by

⛏️ P2SHAdGywN2wBfzQwTo7jGpVnaaNzDznNpTfrS

Merkle Root

089e38f68595dba74a3b24ef91d407131a034312fa861d4c9c1751f21f5a1ae3

Transactions (2)

Coinbase87339da78c59a7…008c2a7b55c54b

1 in → 1 out10.3300 XPM109 B

AdGywN2w…znNpTfrS

e66456e7ee32de…be87eb1813eee3

1 in → 1 out10.3100 XPM157 B

AT75Y59F…25dGF43a

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.

5.651 × 10⁹⁴(95-digit number)

56517255325026607791…18984716558833710419

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

5.651 × 10⁹⁴(95-digit number)

56517255325026607791…18984716558833710419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.651 × 10⁹⁴(95-digit number)

56517255325026607791…18984716558833710421

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

1.130 × 10⁹⁵(96-digit number)

11303451065005321558…37969433117667420839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.130 × 10⁹⁵(96-digit number)

11303451065005321558…37969433117667420841

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

2.260 × 10⁹⁵(96-digit number)

22606902130010643116…75938866235334841679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.260 × 10⁹⁵(96-digit number)

22606902130010643116…75938866235334841681

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

4.521 × 10⁹⁵(96-digit number)

45213804260021286232…51877732470669683359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.521 × 10⁹⁵(96-digit number)

45213804260021286232…51877732470669683361

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

9.042 × 10⁹⁵(96-digit number)

90427608520042572465…03755464941339366719

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