Block #389,833

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/4/2014, 6:19:38 PM · Difficulty 10.4214 · 6,417,251 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

90715331087614ea6e595038fe8f879d7a5b0bf7f4a8e6224416bbd84592f4c9

View on Chainz ↗

Height

#389,833

Difficulty

10.421448

Transactions

Size

1.22 KB

Version

Bits

0a6be3fd

Nonce

2,611

Timestamp

2/4/2014, 6:19:38 PM

Confirmations

6,417,251

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

406ae396ade82e57850dadc0d12d694edd4be1d64a0cb87a12468914a3f373d0

Transactions (5)

Coinbasea11dbc04f4956a…52fcabba5b12ed

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

fb8e4892cf6b0e…7b1f765ffd1f2d

1 in → 2 out7.1724 XPM226 B

ANCU4Pob…nAv97kHk AGjXRvvn…dL3EHMT1

5766ec91a28ada…6af7c6c43d86ec

1 in → 2 out5.1211 XPM226 B

ANa4b2yc…KXu3JPWZ AQyKysvM…vMxfSjur

b1de23ebbd18fb…de4837241bfd21

1 in → 2 out5.1485 XPM226 B

AMU8nEj9…Eo32pqxr AVrnBHbL…Mp62Gc2H

c1cf612e945622…abf1314a66590d

2 in → 2 out3.4403 XPM373 B

AVVBpXqc…KCJkvj9Z AdpsxmtJ…ZWfmvRK9

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.

3.207 × 10⁹⁶(97-digit number)

32073927443300076556…98971046465181909759

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

3.207 × 10⁹⁶(97-digit number)

32073927443300076556…98971046465181909759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.207 × 10⁹⁶(97-digit number)

32073927443300076556…98971046465181909761

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

6.414 × 10⁹⁶(97-digit number)

64147854886600153112…97942092930363819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.414 × 10⁹⁶(97-digit number)

64147854886600153112…97942092930363819521

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

1.282 × 10⁹⁷(98-digit number)

12829570977320030622…95884185860727639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.282 × 10⁹⁷(98-digit number)

12829570977320030622…95884185860727639041

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

2.565 × 10⁹⁷(98-digit number)

25659141954640061244…91768371721455278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.565 × 10⁹⁷(98-digit number)

25659141954640061244…91768371721455278081

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

5.131 × 10⁹⁷(98-digit number)

51318283909280122489…83536743442910556159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.131 × 10⁹⁷(98-digit number)

51318283909280122489…83536743442910556161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.026 × 10⁹⁸(99-digit number)

10263656781856024497…67073486885821112319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #389,833

Cookie Preferences