Block #268,061

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 7:26:31 PM · Difficulty 9.9580 · 6,540,132 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

571f0c946d30218cd1486cfbde7295a616946958e8ec5d83862e72e4c87524da

View on Chainz ↗

Height

#268,061

Difficulty

9.957993

Transactions

Size

767 B

Version

Bits

09f53f02

Nonce

5,967

Timestamp

11/21/2013, 7:26:31 PM

Confirmations

6,540,132

Mined by

⛏️ P2SHALNxQTPbKdodRgiwEdAiX9BGEkCs5xt3Rq

Merkle Root

2482d49cf28ca91041c733436689608b0461476e495bc5050fbc2881187bd1fb

Transactions (3)

Coinbased075d6eb1261fd…374149269151c2

1 in → 1 out10.0900 XPM109 B

ALNxQTPb…Cs5xt3Rq

d47ad4d922c7a2…4124b3dd721fc2

2 in → 2 out57.8600 XPM375 B

ANundQzf…HfYqUXH1 AJxvPqE3…8P7ZyYfR

8e4d3033fa0de4…6d5e588a9bed91

1 in → 1 out1.6622 XPM193 B

AJ4PDgGV…hWMtYWiQ

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.

2.347 × 10⁹⁵(96-digit number)

23477847429550323641…26633434945750519699

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

2.347 × 10⁹⁵(96-digit number)

23477847429550323641…26633434945750519699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.347 × 10⁹⁵(96-digit number)

23477847429550323641…26633434945750519701

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

4.695 × 10⁹⁵(96-digit number)

46955694859100647282…53266869891501039399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.695 × 10⁹⁵(96-digit number)

46955694859100647282…53266869891501039401

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

9.391 × 10⁹⁵(96-digit number)

93911389718201294565…06533739783002078799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.391 × 10⁹⁵(96-digit number)

93911389718201294565…06533739783002078801

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

1.878 × 10⁹⁶(97-digit number)

18782277943640258913…13067479566004157599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.878 × 10⁹⁶(97-digit number)

18782277943640258913…13067479566004157601

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

3.756 × 10⁹⁶(97-digit number)

37564555887280517826…26134959132008315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.756 × 10⁹⁶(97-digit number)

37564555887280517826…26134959132008315201

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 #268,061

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