Block #193,029

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 6:29:38 AM · Difficulty 9.8753 · 6,603,811 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f0221500f2d1215dec70ac11ddc15c3016a7d12780f86a22f7fdbd4dea082249

View on Chainz ↗

Height

#193,029

Difficulty

9.875335

Transactions

Size

2.19 KB

Version

Bits

09e015f2

Nonce

213,986

Timestamp

10/4/2013, 6:29:38 AM

Confirmations

6,603,811

Mined by

⛏️ P2SHAG7BhJFAJWpLoJQxwcJbtoQye4YvhDY6mV

Merkle Root

fb865440814c0d0a0d4ec107d6f4d19ce47fc3b3cabe0aab01f0a5e6e9ca3dbc

Transactions (3)

Coinbase5ad11da91ff6ed…ba4c519c1bfead

1 in → 1 out10.2749 XPM109 B

AG7BhJFA…YvhDY6mV

f4f38c0c0f09e0…7646e8a48b44af

8 in → 2 out24.0983 XPM1.23 KB

AQE3UodM…MvcJ4cF3 AJ1eBrQN…TvS73b6w

f8c34bf0dcf4ed…67c9fad41b4735

5 in → 1 out3.1000 XPM786 B

AR9PyxxC…xiMM8SDu

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.

6.275 × 10⁹⁰(91-digit number)

62750897795920354196…27240731126318967799

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

6.275 × 10⁹⁰(91-digit number)

62750897795920354196…27240731126318967799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.275 × 10⁹⁰(91-digit number)

62750897795920354196…27240731126318967801

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

1.255 × 10⁹¹(92-digit number)

12550179559184070839…54481462252637935599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.255 × 10⁹¹(92-digit number)

12550179559184070839…54481462252637935601

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

2.510 × 10⁹¹(92-digit number)

25100359118368141678…08962924505275871199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.510 × 10⁹¹(92-digit number)

25100359118368141678…08962924505275871201

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

5.020 × 10⁹¹(92-digit number)

50200718236736283357…17925849010551742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.020 × 10⁹¹(92-digit number)

50200718236736283357…17925849010551742401

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

1.004 × 10⁹²(93-digit number)

10040143647347256671…35851698021103484799

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