Block #143,011

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 8:46:34 AM · Difficulty 9.8373 · 6,646,730 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fbcc58c182364692a5fd306aa60559aaf818185c6c51f70d047e2305af331e0c

View on Chainz ↗

Height

#143,011

Difficulty

9.837339

Transactions

Size

200 B

Version

Bits

09d65bd2

Nonce

7,894

Timestamp

8/31/2013, 8:46:34 AM

Confirmations

6,646,730

Merkle Root

f60e8e31ef88b03246583f2f01fed10242ddb38691a544f0e42d4200accd9b1b

Transactions (1)

Coinbasef60e8e31ef88b0…2d4200accd9b1b

1 in → 1 out10.3200 XPM109 B

AK9J6Tuq…Hwb3nQwE

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.

1.313 × 10⁹⁷(98-digit number)

13136175745153597785…44483808367365753199

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

1.313 × 10⁹⁷(98-digit number)

13136175745153597785…44483808367365753199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.313 × 10⁹⁷(98-digit number)

13136175745153597785…44483808367365753201

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

2.627 × 10⁹⁷(98-digit number)

26272351490307195571…88967616734731506399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.627 × 10⁹⁷(98-digit number)

26272351490307195571…88967616734731506401

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

5.254 × 10⁹⁷(98-digit number)

52544702980614391142…77935233469463012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.254 × 10⁹⁷(98-digit number)

52544702980614391142…77935233469463012801

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

1.050 × 10⁹⁸(99-digit number)

10508940596122878228…55870466938926025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.050 × 10⁹⁸(99-digit number)

10508940596122878228…55870466938926025601

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

2.101 × 10⁹⁸(99-digit number)

21017881192245756457…11740933877852051199

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