Block #253,644

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 6:35:14 AM · Difficulty 9.9724 · 6,560,590 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3eb1cba1dc1b29d2544230dc470491b3e298508c4af2abb5bd2c9b30d1c74c82

View on Chainz ↗

Height

#253,644

Difficulty

9.972356

Transactions

Size

61.97 KB

Version

Bits

09f8ec54

Nonce

38,124

Timestamp

11/10/2013, 6:35:14 AM

Confirmations

6,560,590

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

5fcf4fb6880ab7fe97c0ffe9044d083ddad4af60f7d5f4ba32d928d5ed377c3b

Transactions (5)

Coinbaseb23bb8702f0c70…100f78b237c9e6

1 in → 2 out10.7100 XPM141 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

bc062011b2fdee…501d97c0e2c2e7

86 in → 2 out726.0894 XPM12.50 KB

Adu7pfdV…TqXHioKm AN45xKJb…jzPnBV6L

8b3a653b323aef…5a4ab03dd49163

74 in → 2 out10.0100 XPM10.77 KB

AcEFyuUW…yx3jSZbj Aaxkq86R…J2x8n4Yd

c7de29be99053d…b79ffbca76e6d9

89 in → 2 out10.0100 XPM12.95 KB

AZBSj7L2…zazg578a Aaxkq86R…J2x8n4Yd

b05f0980c46e5e…8554e941b0d4e0

176 in → 2 out10.0100 XPM25.52 KB

AQi4vgMd…Gd8NVsJR Aaxkq86R…J2x8n4Yd

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.

1.284 × 10⁹⁵(96-digit number)

12841743361872286321…31134665076457225199

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

1.284 × 10⁹⁵(96-digit number)

12841743361872286321…31134665076457225199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.284 × 10⁹⁵(96-digit number)

12841743361872286321…31134665076457225201

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

2.568 × 10⁹⁵(96-digit number)

25683486723744572642…62269330152914450399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.568 × 10⁹⁵(96-digit number)

25683486723744572642…62269330152914450401

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

5.136 × 10⁹⁵(96-digit number)

51366973447489145284…24538660305828900799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.136 × 10⁹⁵(96-digit number)

51366973447489145284…24538660305828900801

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

1.027 × 10⁹⁶(97-digit number)

10273394689497829056…49077320611657801599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.027 × 10⁹⁶(97-digit number)

10273394689497829056…49077320611657801601

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

2.054 × 10⁹⁶(97-digit number)

20546789378995658113…98154641223315603199

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 #253,644

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