Block #193,751

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 5:20:14 PM · Difficulty 9.8772 · 6,601,686 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

801955767b852d2ddb144ee851dcc372da467a22ce71fd4f106bfba9a5a9914f

View on Chainz ↗

Height

#193,751

Difficulty

9.877213

Transactions

Size

1.08 KB

Version

Bits

09e09108

Nonce

127,481

Timestamp

10/4/2013, 5:20:14 PM

Confirmations

6,601,686

Mined by

⛏️ P2SHATboKVD2SWwNv3ZJPSB6qg7jz3jVUvq4K8

Merkle Root

633deed7394310866e75c14699fa909a84337451244c977d1d9e77822585a228

Transactions (5)

Coinbasec792dd805bdafe…7e40cedcf8c07b

1 in → 1 out10.2700 XPM109 B

ATboKVD2…jVUvq4K8

9c88b9959f3c75…70f3f6ce03fd9a

1 in → 2 out10.2300 XPM226 B

AYYULu8V…HPcDRDSH AXKEUdSD…fHdbr1qr

4af12d2e957fa4…08b3c94b684519

1 in → 2 out8.2161 XPM225 B

AUyoQ7hR…WpUfYm7e AXZvTo9z…YBDPsrv2

6ab5b416c48a2b…4f4bdab6d64da5

1 in → 2 out7.3859 XPM226 B

AUaD4rGJ…cEdnwTEF AS2jrpr2…pJfe63jp

a2280b2b3e9777…2878a78deb84fa

1 in → 2 out2.4387 XPM226 B

AZY3P1pS…XwuzukzA AJv5WoqT…tqCRQqFk

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.

5.071 × 10⁹⁵(96-digit number)

50714611235827673224…61524029130906168319

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

5.071 × 10⁹⁵(96-digit number)

50714611235827673224…61524029130906168319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.071 × 10⁹⁵(96-digit number)

50714611235827673224…61524029130906168321

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

1.014 × 10⁹⁶(97-digit number)

10142922247165534644…23048058261812336639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.014 × 10⁹⁶(97-digit number)

10142922247165534644…23048058261812336641

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

2.028 × 10⁹⁶(97-digit number)

20285844494331069289…46096116523624673279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.028 × 10⁹⁶(97-digit number)

20285844494331069289…46096116523624673281

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

4.057 × 10⁹⁶(97-digit number)

40571688988662138579…92192233047249346559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.057 × 10⁹⁶(97-digit number)

40571688988662138579…92192233047249346561

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

8.114 × 10⁹⁶(97-digit number)

81143377977324277158…84384466094498693119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.114 × 10⁹⁶(97-digit number)

81143377977324277158…84384466094498693121

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