Block #394,839

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 6:14:14 AM · Difficulty 10.4196 · 6,414,456 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0549840a06cfbdac12a3fbc6abcc4420d43f7dca38f4f08a515e26e4c53b73a

View on Chainz ↗

Height

#394,839

Difficulty

10.419645

Transactions

Size

674 B

Version

Bits

0a6b6dd9

Nonce

59,694

Timestamp

2/8/2014, 6:14:14 AM

Confirmations

6,414,456

Mined by

⛏️ WAc2JYASPQD7vWBs42nkRqpCmFvtcBL5PEW

Merkle Root

ec115d32533f04f25c8a6db91d8c3bc95790ca2a0cb2a7b00c9cd05c65d98b49

Transactions (3)

Coinbased317f6384d6b3f…39baf3ef05de05

1 in → 2 out9.2200 XPM131 B

Ac2JYASP…tcBL5PEW AJno7LX2…vo4wdWtY

73ad4c96bc1142…5c42121e1f0dae

1 in → 2 out5.0923 XPM225 B

Aatjfi4Q…22oxfLqM AT7nZXYL…LQ7L3L4N

e5ad3b57eeb9ab…8ae42cbb3ded05

1 in → 2 out4.0986 XPM226 B

AGjXRvvn…dL3EHMT1 Aa7jZ745…SRZoa6Rg

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.

3.693 × 10⁹⁹(100-digit number)

36939458814351263508…57919014709965351499

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

3.693 × 10⁹⁹(100-digit number)

36939458814351263508…57919014709965351499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.693 × 10⁹⁹(100-digit number)

36939458814351263508…57919014709965351501

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

7.387 × 10⁹⁹(100-digit number)

73878917628702527017…15838029419930702999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.387 × 10⁹⁹(100-digit number)

73878917628702527017…15838029419930703001

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

1.477 × 10¹⁰⁰(101-digit number)

14775783525740505403…31676058839861405999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.477 × 10¹⁰⁰(101-digit number)

14775783525740505403…31676058839861406001

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

2.955 × 10¹⁰⁰(101-digit number)

29551567051481010807…63352117679722811999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.955 × 10¹⁰⁰(101-digit number)

29551567051481010807…63352117679722812001

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

5.910 × 10¹⁰⁰(101-digit number)

59103134102962021614…26704235359445623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.910 × 10¹⁰⁰(101-digit number)

59103134102962021614…26704235359445624001

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 #394,839

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