Block #272,902

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 12:51:42 PM · Difficulty 9.9536 · 6,536,747 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

054f519fd617b9b4f32f7a91ac23074a10f856058124cff04ba5e4b3ca6780b3

View on Chainz ↗

Height

#272,902

Difficulty

9.953571

Transactions

Size

1.44 KB

Version

Bits

09f41d37

Nonce

3,710

Timestamp

11/25/2013, 12:51:42 PM

Confirmations

6,536,747

Mined by

⛏️ P2SHAcjBsJrEyaf5G9d3ZbpqrHKMFAH7pp8fdW

Merkle Root

149a30994b9d9b48f606636bf90171841731ddc308dc0d88649efffb243e7917

Transactions (4)

Coinbase616829d67d5f54…812c8e6f4a642d

1 in → 1 out10.2000 XPM109 B

AcjBsJrE…H7pp8fdW

d4c2d06442075e…28f8cc57d38aa6

1 in → 2 out31.9010 XPM226 B

AeWYPqEN…okHWWzAV AHufpinY…g9feViEj

0bbbf964c9d462…88f6b0517e32ec

3 in → 2 out1.0103 XPM523 B

AQfxT7zj…zRy1ZiVs AJLkctkZ…PscmbEjM

f47ea2780a9f97…81b6f039402a29

3 in → 2 out41.4851 XPM523 B

Ack313kV…Ln1FHSJT AGx8f6uT…oS28QCLW

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.

8.209 × 10⁹¹(92-digit number)

82098068340744246760…06860953336145155199

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

8.209 × 10⁹¹(92-digit number)

82098068340744246760…06860953336145155199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.209 × 10⁹¹(92-digit number)

82098068340744246760…06860953336145155201

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

1.641 × 10⁹²(93-digit number)

16419613668148849352…13721906672290310399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.641 × 10⁹²(93-digit number)

16419613668148849352…13721906672290310401

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

3.283 × 10⁹²(93-digit number)

32839227336297698704…27443813344580620799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.283 × 10⁹²(93-digit number)

32839227336297698704…27443813344580620801

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

6.567 × 10⁹²(93-digit number)

65678454672595397408…54887626689161241599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.567 × 10⁹²(93-digit number)

65678454672595397408…54887626689161241601

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

1.313 × 10⁹³(94-digit number)

13135690934519079481…09775253378322483199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.313 × 10⁹³(94-digit number)

13135690934519079481…09775253378322483201

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 #272,902

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