Block #111,397

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/11/2013, 10:45:57 AM · Difficulty 9.7071 · 6,691,126 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cba6103b19b79b9c263296fb16538ab6c0a087816ef103c857a7f3aa2054be01

View on Chainz ↗

Height

#111,397

Difficulty

9.707083

Transactions

Size

5.06 KB

Version

Bits

09b50361

Nonce

5,048

Timestamp

8/11/2013, 10:45:57 AM

Confirmations

6,691,126

Mined by

⛏️ P2SHAL2EWWZmctFoTxS7QgAsvUyr8tCwsD5iKb

Merkle Root

f6b5f298608ea40f45d8b529f11d90e4c4bb09566e82df411291dd266476ad87

Transactions (2)

Coinbase53d6bf2e115e09…74d0ee4ec0a545

1 in → 1 out10.6500 XPM109 B

AL2EWWZm…CwsD5iKb

65ec14e251478a…dcac64dc070cc1

43 in → 2 out462.8300 XPM4.86 KB

ALMKdpef…ehXinMdh AdNeXXkk…QpfXAns4

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.

5.853 × 10⁹⁹(100-digit number)

58535403607177027964…01651926025353726599

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

5.853 × 10⁹⁹(100-digit number)

58535403607177027964…01651926025353726599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.853 × 10⁹⁹(100-digit number)

58535403607177027964…01651926025353726601

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

1.170 × 10¹⁰⁰(101-digit number)

11707080721435405592…03303852050707453199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.170 × 10¹⁰⁰(101-digit number)

11707080721435405592…03303852050707453201

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

2.341 × 10¹⁰⁰(101-digit number)

23414161442870811185…06607704101414906399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.341 × 10¹⁰⁰(101-digit number)

23414161442870811185…06607704101414906401

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

4.682 × 10¹⁰⁰(101-digit number)

46828322885741622371…13215408202829812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.682 × 10¹⁰⁰(101-digit number)

46828322885741622371…13215408202829812801

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

9.365 × 10¹⁰⁰(101-digit number)

93656645771483244742…26430816405659625599

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