Block #390,734

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/5/2014, 8:47:11 AM · Difficulty 10.4255 · 6,418,883 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

703186b98b9761ab660349f87ba1062a159b2ef49ffe6e28098643c897959a0b

View on Chainz ↗

Height

#390,734

Difficulty

10.425507

Transactions

Size

1.68 KB

Version

Bits

0a6cee03

Nonce

1,679

Timestamp

2/5/2014, 8:47:11 AM

Confirmations

6,418,883

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fecb06a3decf5b95121a68d97509cb3bf00e0c10ba5eae2eb2faa894e92467fd

Transactions (2)

Coinbase9ce91a8ec2ce8b…151523f601bf2a

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

6e0cd4e8185e82…b4efefea34d2de

9 in → 7 out19.2810 XPM1.48 KB

AQtNDSnb…MWwodF2D AeKNrjNj…1NEq95Ta AHG4xSSE…uGniXy6K AG75JD8M…YE8Hjvb7 AMurAYrb…3iomaSF2

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.

1.485 × 10⁹⁷(98-digit number)

14858416540026671975…82362134832135576639

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

1.485 × 10⁹⁷(98-digit number)

14858416540026671975…82362134832135576639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.485 × 10⁹⁷(98-digit number)

14858416540026671975…82362134832135576641

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

2.971 × 10⁹⁷(98-digit number)

29716833080053343950…64724269664271153279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.971 × 10⁹⁷(98-digit number)

29716833080053343950…64724269664271153281

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

5.943 × 10⁹⁷(98-digit number)

59433666160106687900…29448539328542306559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.943 × 10⁹⁷(98-digit number)

59433666160106687900…29448539328542306561

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

1.188 × 10⁹⁸(99-digit number)

11886733232021337580…58897078657084613119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.188 × 10⁹⁸(99-digit number)

11886733232021337580…58897078657084613121

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

2.377 × 10⁹⁸(99-digit number)

23773466464042675160…17794157314169226239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.377 × 10⁹⁸(99-digit number)

23773466464042675160…17794157314169226241

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

4.754 × 10⁹⁸(99-digit number)

47546932928085350320…35588314628338452479

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 #390,734

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