Block #391,783

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 1:45:59 AM · Difficulty 10.4289 · 6,411,856 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f094db93b751cfd277fcaae630304642e1fa81c502065570bfcb572d2340c3f

View on Chainz ↗

Height

#391,783

Difficulty

10.428862

Transactions

Size

835 B

Version

Bits

0a6dc9e9

Nonce

201,482

Timestamp

2/6/2014, 1:45:59 AM

Confirmations

6,411,856

Mined by

⛏️ gAcs9SHrkBk52E7r7T3v7yemDoFQJSB8SFG

Merkle Root

105284b6b800b65a6822d09715c2a421b480477e300b0ebb4761066b023f82c7

Transactions (1)

Coinbase105284b6b800b6…61066b023f82c7

1 in → 20 out9.1800 XPM743 B

Acs9SHrk…QJSB8SFG APJPNQaM…8nyTxzkW AW2fas42…gGAHYdHj AZqjMFvv…G8aw2zC8 AH3Te5We…Q6rEnE3e

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.

1.074 × 10⁹⁹(100-digit number)

10740984447453686863…39645208152698356479

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

1.074 × 10⁹⁹(100-digit number)

10740984447453686863…39645208152698356479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.074 × 10⁹⁹(100-digit number)

10740984447453686863…39645208152698356481

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

2.148 × 10⁹⁹(100-digit number)

21481968894907373726…79290416305396712959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.148 × 10⁹⁹(100-digit number)

21481968894907373726…79290416305396712961

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

4.296 × 10⁹⁹(100-digit number)

42963937789814747453…58580832610793425919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.296 × 10⁹⁹(100-digit number)

42963937789814747453…58580832610793425921

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

8.592 × 10⁹⁹(100-digit number)

85927875579629494906…17161665221586851839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.592 × 10⁹⁹(100-digit number)

85927875579629494906…17161665221586851841

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

1.718 × 10¹⁰⁰(101-digit number)

17185575115925898981…34323330443173703679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.718 × 10¹⁰⁰(101-digit number)

17185575115925898981…34323330443173703681

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