Block #378,293

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 5:19:56 PM · Difficulty 10.4219 · 6,416,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95e22cb2e88d84b5012d59f866d6c773656d97ebe38e75916abc04431eb14718

View on Chainz ↗

Height

#378,293

Difficulty

10.421856

Transactions

Size

884 B

Version

Bits

0a6bfec2

Nonce

44,464

Timestamp

1/27/2014, 5:19:56 PM

Confirmations

6,416,651

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

98ec1ed12fe38083434480ed7f0336af5f9d1e9b3c08ba14f4dd9b5ea2eb0ea9

Transactions (4)

Coinbase7e753ba2c078e5…923a3736baefab

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

e992475e4c4a1b…b6d3d14347d37f

1 in → 2 out8.1695 XPM227 B

AUHMQvdo…AJ1jGAvW AKxXt2sk…ZZmgfgbD

1a00b20d7da179…186d464fb14242

1 in → 2 out6.1346 XPM225 B

AcNpXXXw…FnVtBFco AepMNKRZ…1iLuTJuu

7f9b85f6f6b5f4…17e4fe7bda6d6d

1 in → 2 out1.6846 XPM227 B

Ac8to8Cx…dUhTEYMJ AJT33oDW…gPPRXbKn

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.

3.100 × 10⁹¹(92-digit number)

31004044159582330282…13764999972961349969

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

3.100 × 10⁹¹(92-digit number)

31004044159582330282…13764999972961349969

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.100 × 10⁹¹(92-digit number)

31004044159582330282…13764999972961349971

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

6.200 × 10⁹¹(92-digit number)

62008088319164660564…27529999945922699939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.200 × 10⁹¹(92-digit number)

62008088319164660564…27529999945922699941

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

1.240 × 10⁹²(93-digit number)

12401617663832932112…55059999891845399879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.240 × 10⁹²(93-digit number)

12401617663832932112…55059999891845399881

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

2.480 × 10⁹²(93-digit number)

24803235327665864225…10119999783690799759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.480 × 10⁹²(93-digit number)

24803235327665864225…10119999783690799761

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

4.960 × 10⁹²(93-digit number)

49606470655331728451…20239999567381599519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.960 × 10⁹²(93-digit number)

49606470655331728451…20239999567381599521

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