Block #237,179

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 9:36:39 PM · Difficulty 9.9494 · 6,558,702 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ac55908d6edeea69887ddb5e183dd6fc5baeed729d7304b3dc6c475d038df73

View on Chainz ↗

Height

#237,179

Difficulty

9.949362

Transactions

Size

1.53 KB

Version

Bits

09f30960

Nonce

9,644

Timestamp

10/31/2013, 9:36:39 PM

Confirmations

6,558,702

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

0b9cbd355ca573fd4a36687b9de740b7ca472ad292125fd737d4d0736af266f7

Transactions (3)

Coinbase551af0ad3eb68a…2b4ea6eef9ba83

1 in → 2 out10.1200 XPM137 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

4311d717666407…2fa92bc36d694f

1 in → 2 out10.0900 XPM227 B

AVYA5FSq…eeZm8KGY ARqwyDpz…7D5mpuj9

03a181e9d4968e…269e850638e69f

7 in → 2 out50.2258 XPM1.09 KB

AKPyyNoA…zkEJfJN9 AUiU4uvm…468FRpVA

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.

2.161 × 10⁹⁷(98-digit number)

21616252907103826221…54831386472911064639

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

2.161 × 10⁹⁷(98-digit number)

21616252907103826221…54831386472911064639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.161 × 10⁹⁷(98-digit number)

21616252907103826221…54831386472911064641

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

4.323 × 10⁹⁷(98-digit number)

43232505814207652443…09662772945822129279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.323 × 10⁹⁷(98-digit number)

43232505814207652443…09662772945822129281

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

8.646 × 10⁹⁷(98-digit number)

86465011628415304887…19325545891644258559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.646 × 10⁹⁷(98-digit number)

86465011628415304887…19325545891644258561

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

1.729 × 10⁹⁸(99-digit number)

17293002325683060977…38651091783288517119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.729 × 10⁹⁸(99-digit number)

17293002325683060977…38651091783288517121

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

3.458 × 10⁹⁸(99-digit number)

34586004651366121955…77302183566577034239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.458 × 10⁹⁸(99-digit number)

34586004651366121955…77302183566577034241

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