Block #474,275

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 11:36:38 AM · Difficulty 10.4496 · 6,335,906 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c6343d7ba89c9e043f4d38104f214dd8115eceefd4ce50b1ab476c70e788366

View on Chainz ↗

Height

#474,275

Difficulty

10.449600

Transactions

Size

13.15 KB

Version

Bits

0a7318f5

Nonce

107,081

Timestamp

4/4/2014, 11:36:38 AM

Confirmations

6,335,906

Mined by

⛏️ <aS>AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e2b4875e8be5dd18e0025d97d7fdd002182cb14710bdc59cddd79653add03ff8

Transactions (4)

Coinbasee49459702ea6d9…d3bce65ce9b4cf

1 in → 18 out9.1400 XPM675 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AGKhfQo2…h7fBXLX6

ddbfeb5a54c07d…604cfd8d24084d

9 in → 11 out37.0602 XPM1.54 KB

APEpJtDK…yx7xJDz7 ARHXPaf8…PwwQ8Qxi AM6JvF6Y…u5DULnSo AeKNrjNj…1NEq95Ta AGRJf5c9…j28JnLsV

8b9fedc9ebb60a…37152bd842476e

73 in → 2 out28.1073 XPM10.64 KB

AeNGwRxW…APCvDudG AVvFfVNY…C5VA89ZD

c898b49fc2b5f1…af9a5348346cee

1 in → 2 out5.5577 XPM227 B

AbR72DuD…EY332v4m AbMH1CXh…4CZZ7jJJ

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.

2.919 × 10⁹⁶(97-digit number)

29199950335011794077…77698619512396239999

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

2.919 × 10⁹⁶(97-digit number)

29199950335011794077…77698619512396239999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.919 × 10⁹⁶(97-digit number)

29199950335011794077…77698619512396240001

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

5.839 × 10⁹⁶(97-digit number)

58399900670023588155…55397239024792479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.839 × 10⁹⁶(97-digit number)

58399900670023588155…55397239024792480001

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

1.167 × 10⁹⁷(98-digit number)

11679980134004717631…10794478049584959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.167 × 10⁹⁷(98-digit number)

11679980134004717631…10794478049584960001

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

2.335 × 10⁹⁷(98-digit number)

23359960268009435262…21588956099169919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.335 × 10⁹⁷(98-digit number)

23359960268009435262…21588956099169920001

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

4.671 × 10⁹⁷(98-digit number)

46719920536018870524…43177912198339839999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.671 × 10⁹⁷(98-digit number)

46719920536018870524…43177912198339840001

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

Block #474,275

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