Block #268,054

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 7:13:28 PM · Difficulty 9.9581 · 6,574,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b6ccdde598835a939aa6aeb2a542d3c4b3f98b62c2c7aaf015710f0af1d731b

View on Chainz ↗

Height

#268,054

Difficulty

9.958054

Transactions

Size

906 B

Version

Bits

09f54304

Nonce

52,509

Timestamp

11/21/2013, 7:13:28 PM

Confirmations

6,574,517

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

cf77beee0a3073d7bb6a693867b599ec6b2a2c8b2a3b2c79a5bd360f9b4284c8

Transactions (2)

Coinbaseb6798659846ec6…da6d9404c396e3

1 in → 2 out10.0800 XPM142 B

AdGRRh1e…QmctLb24 ALfEGCwh…VawujfMm

6571207baa8bb2…fda34716d78fa1

4 in → 2 out483.4230 XPM671 B

AdGd5kRg…tauWzQTr AaG9aCiw…hbkMWkbX

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.

2.433 × 10¹⁰¹(102-digit number)

24332534191414853962…71013368717862594759

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

2.433 × 10¹⁰¹(102-digit number)

24332534191414853962…71013368717862594759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.433 × 10¹⁰¹(102-digit number)

24332534191414853962…71013368717862594761

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

4.866 × 10¹⁰¹(102-digit number)

48665068382829707925…42026737435725189519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.866 × 10¹⁰¹(102-digit number)

48665068382829707925…42026737435725189521

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

9.733 × 10¹⁰¹(102-digit number)

97330136765659415850…84053474871450379039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.733 × 10¹⁰¹(102-digit number)

97330136765659415850…84053474871450379041

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

1.946 × 10¹⁰²(103-digit number)

19466027353131883170…68106949742900758079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.946 × 10¹⁰²(103-digit number)

19466027353131883170…68106949742900758081

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

3.893 × 10¹⁰²(103-digit number)

38932054706263766340…36213899485801516159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.893 × 10¹⁰²(103-digit number)

38932054706263766340…36213899485801516161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #268,054

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