Block #1,542,154

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2016, 7:25:14 AM · Difficulty 10.6489 · 5,266,824 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

355641969f13d06cfd7adafeca03f0292694753f38266d627ce4229ae546a137

View on Chainz ↗

Height

#1,542,154

Difficulty

10.648907

Transactions

Size

18.33 KB

Version

Bits

0aa61ebd

Nonce

2,085,413,957

Timestamp

4/15/2016, 7:25:14 AM

Confirmations

5,266,824

Mined by

⛏️ P2SHAQZXhrPW2qPn1bS6hFJFGn8g4FjPDbdX29

Merkle Root

912a76799c230ad2304b6c81a3080e9c2f134b9a7b8b404565bd8261040789a7

Transactions (2)

Coinbaseeafb79fdc32e34…df3a9bd7b43dfa

1 in → 1 out9.0100 XPM110 B

AQZXhrPW…jPDbdX29

fb649c42ddfc02…e1dc31d37534b0

125 in → 2 out756.3740 XPM18.13 KB

AUNKcm5A…wBqmMSFg AQHE5e6H…xDwU3vYU

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.

7.538 × 10⁹⁵(96-digit number)

75382533404773609367…33211325326204090879

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

7.538 × 10⁹⁵(96-digit number)

75382533404773609367…33211325326204090879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.538 × 10⁹⁵(96-digit number)

75382533404773609367…33211325326204090881

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

1.507 × 10⁹⁶(97-digit number)

15076506680954721873…66422650652408181759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.507 × 10⁹⁶(97-digit number)

15076506680954721873…66422650652408181761

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

3.015 × 10⁹⁶(97-digit number)

30153013361909443747…32845301304816363519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.015 × 10⁹⁶(97-digit number)

30153013361909443747…32845301304816363521

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

6.030 × 10⁹⁶(97-digit number)

60306026723818887494…65690602609632727039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.030 × 10⁹⁶(97-digit number)

60306026723818887494…65690602609632727041

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

1.206 × 10⁹⁷(98-digit number)

12061205344763777498…31381205219265454079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.206 × 10⁹⁷(98-digit number)

12061205344763777498…31381205219265454081

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 #1,542,154

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