Block #1,971,752

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2017, 2:30:06 PM · Difficulty 10.7541 · 4,846,008 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

818a6197e1f0fe0083a94120ecfed4810b356069bd1606d9f2c074b88bb24e43

View on Chainz ↗

Height

#1,971,752

Difficulty

10.754059

Transactions

Size

61.19 KB

Version

Bits

0ac10a06

Nonce

169,640,778

Timestamp

2/6/2017, 2:30:06 PM

Confirmations

4,846,008

Mined by

⛏️ P2SHAad4GQ1MeW4jfjFFEz6fsFeWKcZHi8hdYH

Merkle Root

b2fd4fa99a1419322bec0df908730162c0f2abb64601f6c4f11b4f92cb5f5605

Transactions (3)

Coinbasef73063f296a785…8344af401bdd14

1 in → 1 out9.2600 XPM109 B

Aad4GQ1M…ZHi8hdYH

f22a164ed0c978…c5460e58e53f94

416 in → 2 out5000.0100 XPM60.20 KB

AWXmZieK…aDEYz9kj AKAHKtud…mQBq4Q8J

9cb7f6a03bc03c…1ab6c931e88634

5 in → 2 out132.4087 XPM818 B

AZYch58b…7tKKy2Sb AKGxoSP8…8oH3hVLd

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.

1.438 × 10⁹⁴(95-digit number)

14389863592551243181…06054094653221267179

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

1.438 × 10⁹⁴(95-digit number)

14389863592551243181…06054094653221267179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.438 × 10⁹⁴(95-digit number)

14389863592551243181…06054094653221267181

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

2.877 × 10⁹⁴(95-digit number)

28779727185102486363…12108189306442534359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.877 × 10⁹⁴(95-digit number)

28779727185102486363…12108189306442534361

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

5.755 × 10⁹⁴(95-digit number)

57559454370204972727…24216378612885068719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.755 × 10⁹⁴(95-digit number)

57559454370204972727…24216378612885068721

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

1.151 × 10⁹⁵(96-digit number)

11511890874040994545…48432757225770137439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.151 × 10⁹⁵(96-digit number)

11511890874040994545…48432757225770137441

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

2.302 × 10⁹⁵(96-digit number)

23023781748081989091…96865514451540274879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.302 × 10⁹⁵(96-digit number)

23023781748081989091…96865514451540274881

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 #1,971,752

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