Block #268,468

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 4:08:48 AM · Difficulty 9.9571 · 6,540,867 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea3f0a626b944ee19d6da6d02877690d500b7eb0a0eacf4df6296cf58729494e

View on Chainz ↗

Height

#268,468

Difficulty

9.957060

Transactions

Size

1.91 KB

Version

Bits

09f501db

Nonce

507,293

Timestamp

11/22/2013, 4:08:48 AM

Confirmations

6,540,867

Mined by

⛏️ aR.AGHJDQA6MYJdWVwCF6BCcGo8ZohCLcZMXq

Merkle Root

0656fcd17ec51317e7f57edd9fb341a31ba01a7332484a120164b4331ffe234a

Transactions (1)

Coinbase0656fcd17ec513…64b4331ffe234a

1 in → 53 out10.0500 XPM1.82 KB

AGHJDQA6…hCLcZMXq AQbu7mdU…kaYDc9Lq AKXeSXzu…yeuNjvhB Aafo7GUB…1DzYV5Cs APZy8y6E…QZaGQjfp

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.

5.054 × 10⁹⁵(96-digit number)

50546001813869411266…11646749066742251519

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

5.054 × 10⁹⁵(96-digit number)

50546001813869411266…11646749066742251519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.054 × 10⁹⁵(96-digit number)

50546001813869411266…11646749066742251521

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

1.010 × 10⁹⁶(97-digit number)

10109200362773882253…23293498133484503039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.010 × 10⁹⁶(97-digit number)

10109200362773882253…23293498133484503041

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

2.021 × 10⁹⁶(97-digit number)

20218400725547764506…46586996266969006079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.021 × 10⁹⁶(97-digit number)

20218400725547764506…46586996266969006081

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

4.043 × 10⁹⁶(97-digit number)

40436801451095529013…93173992533938012159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.043 × 10⁹⁶(97-digit number)

40436801451095529013…93173992533938012161

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

8.087 × 10⁹⁶(97-digit number)

80873602902191058026…86347985067876024319

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

Block #268,468

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