Block #143,012

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 8:47:49 AM · Difficulty 9.8374 · 6,646,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8cab0ea1f6d41bfc35d0b980d40067cc4fa9a39c22826745c5fb10447dc89aec

View on Chainz ↗

Height

#143,012

Difficulty

9.837368

Transactions

Size

577 B

Version

Bits

09d65dba

Nonce

272,745

Timestamp

8/31/2013, 8:47:49 AM

Confirmations

6,646,511

Merkle Root

a1950d4e9c1b71f7148f7f076526672f644b15f0c7dcb830dada0f13c6d338e1

Transactions (2)

Coinbase349694fd01108c…a2354aae62e744

1 in → 1 out10.3300 XPM100 B

AbGkvdxH…oihMdBXd

fdf8648879a17a…cfdf025af1337f

3 in → 1 out36.3900 XPM387 B

AX9US9BG…VNQafoJ4

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.

7.962 × 10⁹³(94-digit number)

79624565145995561455…93886772596938820599

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

7.962 × 10⁹³(94-digit number)

79624565145995561455…93886772596938820599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.962 × 10⁹³(94-digit number)

79624565145995561455…93886772596938820601

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

1.592 × 10⁹⁴(95-digit number)

15924913029199112291…87773545193877641199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.592 × 10⁹⁴(95-digit number)

15924913029199112291…87773545193877641201

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

3.184 × 10⁹⁴(95-digit number)

31849826058398224582…75547090387755282399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.184 × 10⁹⁴(95-digit number)

31849826058398224582…75547090387755282401

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

6.369 × 10⁹⁴(95-digit number)

63699652116796449164…51094180775510564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.369 × 10⁹⁴(95-digit number)

63699652116796449164…51094180775510564801

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

1.273 × 10⁹⁵(96-digit number)

12739930423359289832…02188361551021129599

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