Block #1,895,253

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/15/2016, 12:19:14 PM · Difficulty 10.7487 · 4,929,245 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d04ebe0f5c1ed5411771b9bae3cd9bf08c48e000b29f706eee1fa6d54580ab1

View on Chainz ↗

Height

#1,895,253

Difficulty

10.748657

Transactions

Size

720 B

Version

Bits

0abfa803

Nonce

284,630,718

Timestamp

12/15/2016, 12:19:14 PM

Confirmations

4,929,245

Mined by

⛏️ P2SHAM5kiNVzN1BWKFQtdviBT1AiyYpPmhsgMZ

Merkle Root

692d92499f13534e20df5825b9756612f7fd2c23b980b2fd96e16bed3d1410f3

Transactions (2)

Coinbase7ead37544e36ec…6928ccf8cde215

1 in → 1 out8.6500 XPM109 B

AM5kiNVz…pPmhsgMZ

f242f3d0547591…803c4ae126050e

3 in → 2 out2.3650 XPM522 B

AQjy1Cgd…J6JXxtev ASMMZz4E…7FeHYYcp

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.

1.173 × 10⁹³(94-digit number)

11732275861166051452…19730802155020518519

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

1.173 × 10⁹³(94-digit number)

11732275861166051452…19730802155020518519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.173 × 10⁹³(94-digit number)

11732275861166051452…19730802155020518521

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

2.346 × 10⁹³(94-digit number)

23464551722332102905…39461604310041037039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.346 × 10⁹³(94-digit number)

23464551722332102905…39461604310041037041

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

4.692 × 10⁹³(94-digit number)

46929103444664205811…78923208620082074079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.692 × 10⁹³(94-digit number)

46929103444664205811…78923208620082074081

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

9.385 × 10⁹³(94-digit number)

93858206889328411623…57846417240164148159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.385 × 10⁹³(94-digit number)

93858206889328411623…57846417240164148161

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

1.877 × 10⁹⁴(95-digit number)

18771641377865682324…15692834480328296319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.877 × 10⁹⁴(95-digit number)

18771641377865682324…15692834480328296321

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 #1,895,253

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