Block #245,824

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 5:21:48 PM · Difficulty 9.9641 · 6,559,520 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

27bd3336d60d25558a57e6e455e6cb67e91114a41fb4a3c62c6667d85911b86c

View on Chainz ↗

Height

#245,824

Difficulty

9.964123

Transactions

Size

2.04 KB

Version

Bits

09f6d0c4

Nonce

46,439

Timestamp

11/5/2013, 5:21:48 PM

Confirmations

6,559,520

Mined by

⛏️ @RyAH8yR9wQ8eGkLmdiG7pdqnWGAY3GmoUBGQ

Merkle Root

e4ada8f6236d639aef37a3e0ee07687e3d60dc35b64a220dba13f49dc34cf6de

Transactions (1)

Coinbasee4ada8f6236d63…13f49dc34cf6de

1 in → 57 out10.0400 XPM1.95 KB

AH8yR9wQ…3GmoUBGQ ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ANUaggy4…MWdrertQ

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.

5.715 × 10⁹⁰(91-digit number)

57158351067174927468…11440933543675670249

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

5.715 × 10⁹⁰(91-digit number)

57158351067174927468…11440933543675670249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.715 × 10⁹⁰(91-digit number)

57158351067174927468…11440933543675670251

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

1.143 × 10⁹¹(92-digit number)

11431670213434985493…22881867087351340499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.143 × 10⁹¹(92-digit number)

11431670213434985493…22881867087351340501

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

2.286 × 10⁹¹(92-digit number)

22863340426869970987…45763734174702680999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.286 × 10⁹¹(92-digit number)

22863340426869970987…45763734174702681001

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

4.572 × 10⁹¹(92-digit number)

45726680853739941974…91527468349405361999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.572 × 10⁹¹(92-digit number)

45726680853739941974…91527468349405362001

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

9.145 × 10⁹¹(92-digit number)

91453361707479883949…83054936698810723999

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