Block #473,734

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 3:05:54 AM · Difficulty 10.4461 · 6,329,654 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95d9311165637e5855d262be500bc3a7d07470cdb6e5c01865df3603ab2cb32e

View on Chainz ↗

Height

#473,734

Difficulty

10.446051

Transactions

Size

839 B

Version

Bits

0a72306d

Nonce

160,403

Timestamp

4/4/2014, 3:05:54 AM

Confirmations

6,329,654

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c26b5defaac4a6860330ec662e68636360b621236e387175b425a7c481ca8b63

Transactions (3)

Coinbaseeebd05a2f9b188…0f1ee7667b3e4f

1 in → 1 out9.1700 XPM116 B

AbwWkWZt…kawDhufa

4278713e47fd43…c7ba40ea44ccef

2 in → 2 out64.7800 XPM373 B

ANAxBkBj…6iRwkxwD AN5UYJAR…rFU2ecNx

39c40cbfb21ace…28c0f91971e4d9

1 in → 4 out9.3800 XPM259 B

ALG6Kwki…JVRCDqef ASvbnyvb…4CP8B7rG AeKNrjNj…1NEq95Ta AHrFNmf8…hpqU2WtU

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.

6.247 × 10⁹⁷(98-digit number)

62472021805111541734…65923718935702253279

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

6.247 × 10⁹⁷(98-digit number)

62472021805111541734…65923718935702253279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.247 × 10⁹⁷(98-digit number)

62472021805111541734…65923718935702253281

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

1.249 × 10⁹⁸(99-digit number)

12494404361022308346…31847437871404506559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.249 × 10⁹⁸(99-digit number)

12494404361022308346…31847437871404506561

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

2.498 × 10⁹⁸(99-digit number)

24988808722044616693…63694875742809013119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.498 × 10⁹⁸(99-digit number)

24988808722044616693…63694875742809013121

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

4.997 × 10⁹⁸(99-digit number)

49977617444089233387…27389751485618026239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.997 × 10⁹⁸(99-digit number)

49977617444089233387…27389751485618026241

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

9.995 × 10⁹⁸(99-digit number)

99955234888178466774…54779502971236052479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.995 × 10⁹⁸(99-digit number)

99955234888178466774…54779502971236052481

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