Block #1,534,494

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 6:52:24 AM · Difficulty 10.6174 · 5,276,273 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b657bb4c18baccd5ba563ccb7395b03eb8f664c9042a41b9152103ede7cd3981

View on Chainz ↗

Height

#1,534,494

Difficulty

10.617386

Transactions

Size

15.02 KB

Version

Bits

0a9e0d06

Nonce

1,189,540,691

Timestamp

4/10/2016, 6:52:24 AM

Confirmations

5,276,273

Mined by

⛏️ P2SHAZhWKBLXKE4vf2qBLo4VE8B85gtv44r1FN

Merkle Root

391beac14215f7dafc59ddd89ea8c9679a9e8db3a2a9601743047eb2b84130b2

Transactions (3)

Coinbased1385f9c7fca2e…a50f3428c77079

1 in → 1 out9.0200 XPM109 B

AZhWKBLX…tv44r1FN

f7eb1a2442e44b…68ab48caeafe67

51 in → 1 out551.9052 XPM7.42 KB

AaDQpgCN…54vKNGkC

5dc88a77aa3673…cfc66f43947e84

51 in → 1 out207.6468 XPM7.41 KB

AXP9Kmrx…4Gdws2jb

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.

1.501 × 10⁹⁵(96-digit number)

15015926601542644785…16530628922401671679

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

1.501 × 10⁹⁵(96-digit number)

15015926601542644785…16530628922401671679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.501 × 10⁹⁵(96-digit number)

15015926601542644785…16530628922401671681

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

3.003 × 10⁹⁵(96-digit number)

30031853203085289570…33061257844803343359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.003 × 10⁹⁵(96-digit number)

30031853203085289570…33061257844803343361

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

6.006 × 10⁹⁵(96-digit number)

60063706406170579141…66122515689606686719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.006 × 10⁹⁵(96-digit number)

60063706406170579141…66122515689606686721

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

1.201 × 10⁹⁶(97-digit number)

12012741281234115828…32245031379213373439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.201 × 10⁹⁶(97-digit number)

12012741281234115828…32245031379213373441

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

2.402 × 10⁹⁶(97-digit number)

24025482562468231656…64490062758426746879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.402 × 10⁹⁶(97-digit number)

24025482562468231656…64490062758426746881

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 #1,534,494

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