Block #100,748

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/6/2013, 7:54:00 AM · Difficulty 9.4364 · 6,702,328 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af2ae5d156d15010d264af673a69583a96fe7b309c805b869ad7354cf5247031

View on Chainz ↗

Height

#100,748

Difficulty

9.436448

Transactions

Size

1.51 KB

Version

Bits

096fbb0d

Nonce

656,941

Timestamp

8/6/2013, 7:54:00 AM

Confirmations

6,702,328

Mined by

⛏️ P2SHAbHaf7WHFV93YPSjXF7MBa3zYuC9yJxF4h

Merkle Root

ce0273f18846e96e1dd88c3bd9a87af00e1f36a7da3b8b65e5f28fa191aa6f4e

Transactions (3)

Coinbaseb4e7c93a1c76fa…d027df9b01ac52

1 in → 1 out11.2300 XPM109 B

AbHaf7WH…C9yJxF4h

525a097cd068ba…4cb94b125c9758

5 in → 2 out10.1413 XPM819 B

AQBCJuNt…TRsYjueP AbRcMdB8…vmaM8MeE

d64999194c53e1…77428af93c3601

3 in → 2 out2.0145 XPM523 B

AMr4SwN4…YiqPJP31 AUT1qxTx…t5B3qd8Z

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.

4.585 × 10⁹⁶(97-digit number)

45851004045107564406…11710236526722290439

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

4.585 × 10⁹⁶(97-digit number)

45851004045107564406…11710236526722290439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.585 × 10⁹⁶(97-digit number)

45851004045107564406…11710236526722290441

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

9.170 × 10⁹⁶(97-digit number)

91702008090215128813…23420473053444580879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.170 × 10⁹⁶(97-digit number)

91702008090215128813…23420473053444580881

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

1.834 × 10⁹⁷(98-digit number)

18340401618043025762…46840946106889161759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.834 × 10⁹⁷(98-digit number)

18340401618043025762…46840946106889161761

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

3.668 × 10⁹⁷(98-digit number)

36680803236086051525…93681892213778323519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.668 × 10⁹⁷(98-digit number)

36680803236086051525…93681892213778323521

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

7.336 × 10⁹⁷(98-digit number)

73361606472172103051…87363784427556647039

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