Block #1,448,158

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2016, 4:14:07 PM · Difficulty 10.7588 · 5,369,612 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6978226ba0da0653fb244e88638857817df18a4da9b6eb40d4876a877c7ed64f

View on Chainz ↗

Height

#1,448,158

Difficulty

10.758768

Transactions

Size

4.63 KB

Version

Bits

0ac23e9a

Nonce

1,285,959,315

Timestamp

2/8/2016, 4:14:07 PM

Confirmations

5,369,612

Mined by

⛏️ P2SHASrpPyeTuW2wXRaVK4ijuA1xmPAKJjMmqU

Merkle Root

f42b3ae165d26c2d872624f888c2dede70c051e0d00ace75581a2d027ffae84e

Transactions (2)

Coinbased98511ce516577…e968a0b17458d3

1 in → 1 out8.6800 XPM110 B

ASrpPyeT…AKJjMmqU

9a0cd57cef881b…4662cbce70622f

30 in → 3 out228.6558 XPM4.44 KB

AULJqW7T…TL2PLdFs AQcjeddP…AoqhXrhG AKhCXkjU…9TcuuKUV

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.

2.688 × 10⁹⁵(96-digit number)

26885656989876270489…11917760425803918719

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

2.688 × 10⁹⁵(96-digit number)

26885656989876270489…11917760425803918719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.688 × 10⁹⁵(96-digit number)

26885656989876270489…11917760425803918721

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

5.377 × 10⁹⁵(96-digit number)

53771313979752540979…23835520851607837439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.377 × 10⁹⁵(96-digit number)

53771313979752540979…23835520851607837441

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

1.075 × 10⁹⁶(97-digit number)

10754262795950508195…47671041703215674879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.075 × 10⁹⁶(97-digit number)

10754262795950508195…47671041703215674881

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

2.150 × 10⁹⁶(97-digit number)

21508525591901016391…95342083406431349759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.150 × 10⁹⁶(97-digit number)

21508525591901016391…95342083406431349761

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

4.301 × 10⁹⁶(97-digit number)

43017051183802032783…90684166812862699519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.301 × 10⁹⁶(97-digit number)

43017051183802032783…90684166812862699521

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 #1,448,158

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