Block #387,116

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 9:42:39 PM · Difficulty 10.4157 · 6,429,525 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a3d21309c66377d486a6b0ef89248074e700b961c409a4881d31fa023ca87f1e

View on Chainz ↗

Height

#387,116

Difficulty

10.415748

Transactions

Size

652 B

Version

Bits

0a6a6e7d

Nonce

23,749,886

Timestamp

2/2/2014, 9:42:39 PM

Confirmations

6,429,525

Mined by

⛏️ P2SHALZ1y6WmjcybCAotgH3C7v4bKQEQkJmJhD

Merkle Root

cce20a604935898b2beab47fd214fd87eb67c1f0195a31fde42ec7ea215a40ca

Transactions (3)

Coinbase74204eace87216…b6709bf7ee7d4f

1 in → 1 out9.2200 XPM110 B

ALZ1y6Wm…EQkJmJhD

801972cd49efda…ffdff8459b7d6a

1 in → 2 out5.0950 XPM226 B

AGbkG9k5…fHBY8wWW Ab3ch7w6…p2PkY25q

e45beb856d171a…ceb2d3efaf6aa5

1 in → 2 out4.1061 XPM226 B

AVubSSJr…kZZ8YfzE ARqf6Rwd…1pxF55hf

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.

2.788 × 10⁹⁴(95-digit number)

27882897619902268528…81287859502352291679

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

2.788 × 10⁹⁴(95-digit number)

27882897619902268528…81287859502352291679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.788 × 10⁹⁴(95-digit number)

27882897619902268528…81287859502352291681

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

5.576 × 10⁹⁴(95-digit number)

55765795239804537057…62575719004704583359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.576 × 10⁹⁴(95-digit number)

55765795239804537057…62575719004704583361

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

1.115 × 10⁹⁵(96-digit number)

11153159047960907411…25151438009409166719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.115 × 10⁹⁵(96-digit number)

11153159047960907411…25151438009409166721

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

2.230 × 10⁹⁵(96-digit number)

22306318095921814823…50302876018818333439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.230 × 10⁹⁵(96-digit number)

22306318095921814823…50302876018818333441

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

4.461 × 10⁹⁵(96-digit number)

44612636191843629646…00605752037636666879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.461 × 10⁹⁵(96-digit number)

44612636191843629646…00605752037636666881

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 #387,116

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