Block #395,377

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 4:42:03 PM · Difficulty 10.4097 · 6,412,610 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f2c88506545d8bac7b4762909a8d841f74532bda40aa53e50978e41d075122b6

View on Chainz ↗

Height

#395,377

Difficulty

10.409668

Transactions

Size

431 B

Version

Bits

0a68e001

Nonce

201,328,509

Timestamp

2/8/2014, 4:42:03 PM

Confirmations

6,412,610

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

981e817ee3e424bd6e54c67e4b704643a1ad18119ce6ac03f55b7da20c34b149

Transactions (2)

Coinbased17e6d89f4c92d…cbac8b60eb147f

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

203a6067a6b4d3…3f98e3367837a6

1 in → 2 out16.2900 XPM225 B

AdNdRQUP…C3CuqHWa ALcBy7MP…nzj2PRxt

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.

1.182 × 10⁹⁵(96-digit number)

11820834616203684968…54358710668355696439

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

1.182 × 10⁹⁵(96-digit number)

11820834616203684968…54358710668355696439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.182 × 10⁹⁵(96-digit number)

11820834616203684968…54358710668355696441

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

2.364 × 10⁹⁵(96-digit number)

23641669232407369936…08717421336711392879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.364 × 10⁹⁵(96-digit number)

23641669232407369936…08717421336711392881

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

4.728 × 10⁹⁵(96-digit number)

47283338464814739872…17434842673422785759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.728 × 10⁹⁵(96-digit number)

47283338464814739872…17434842673422785761

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

9.456 × 10⁹⁵(96-digit number)

94566676929629479745…34869685346845571519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.456 × 10⁹⁵(96-digit number)

94566676929629479745…34869685346845571521

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

1.891 × 10⁹⁶(97-digit number)

18913335385925895949…69739370693691143039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.891 × 10⁹⁶(97-digit number)

18913335385925895949…69739370693691143041

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 #395,377

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