Block #2,098,744

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2017, 9:13:11 PM · Difficulty 10.8616 · 4,732,181 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

268159719734e9b265045619f5c4f456f0dcaa179ac259e8f59648fbf39f8018

View on Chainz ↗

Height

#2,098,744

Difficulty

10.861592

Transactions

Size

2.58 KB

Version

Bits

0adc9147

Nonce

589,011,077

Timestamp

5/3/2017, 9:13:11 PM

Confirmations

4,732,181

Mined by

⛏️ P2SHAey3jMXpR8sXyiqX3zUEJX8i4PNTQjwLu9

Merkle Root

2b26d8d8c0daddef25e0ec6db0a7f6161efeb7ae825f4eeb8f6a52514fffee5f

Transactions (2)

Coinbase4cbd01f69a8471…d0cc6ad9ae7a9c

1 in → 1 out8.5000 XPM109 B

Aey3jMXp…NTQjwLu9

0a0500d91f00f9…db2da24378625a

16 in → 2 out166.3129 XPM2.39 KB

AQZZ3BhW…ZLW7uah6 AFpHJhDK…hyA1PvSQ

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.

1.526 × 10⁹⁴(95-digit number)

15268502279210164050…09818410278956253519

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

1.526 × 10⁹⁴(95-digit number)

15268502279210164050…09818410278956253519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.526 × 10⁹⁴(95-digit number)

15268502279210164050…09818410278956253521

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

3.053 × 10⁹⁴(95-digit number)

30537004558420328100…19636820557912507039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.053 × 10⁹⁴(95-digit number)

30537004558420328100…19636820557912507041

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

6.107 × 10⁹⁴(95-digit number)

61074009116840656200…39273641115825014079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.107 × 10⁹⁴(95-digit number)

61074009116840656200…39273641115825014081

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

1.221 × 10⁹⁵(96-digit number)

12214801823368131240…78547282231650028159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.221 × 10⁹⁵(96-digit number)

12214801823368131240…78547282231650028161

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

2.442 × 10⁹⁵(96-digit number)

24429603646736262480…57094564463300056319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.442 × 10⁹⁵(96-digit number)

24429603646736262480…57094564463300056321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.885 × 10⁹⁵(96-digit number)

48859207293472524960…14189128926600112639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,098,744

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