Block #2,177,896

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2017, 7:39:38 PM · Difficulty 10.9244 · 4,653,288 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

681a4969ded757d55997dbbc56a8cb505913de651cbc6074d768873da0a1e245

View on Chainz ↗

Height

#2,177,896

Difficulty

10.924435

Transactions

Size

652 B

Version

Bits

0aeca7c3

Nonce

1,673,172,914

Timestamp

6/25/2017, 7:39:38 PM

Confirmations

4,653,288

Mined by

⛏️ P2SHAJUhdusxa69rhAAG9CK7unGt5QixBNrdfK

Merkle Root

5b8e9df81eecc155aef701376730b0d225e1997a675789f403bb8d1e57b14bc9

Transactions (3)

Coinbase63e992a9c1b9d7…8e100b2f90ef5f

1 in → 1 out8.3900 XPM109 B

AJUhdusx…ixBNrdfK

8ec04be41a924a…6949fe6d46a80d

1 in → 2 out99249.7548 XPM226 B

AQSeeraN…rEqLZBtN AQSgj4pE…bZvBeace

0964ba94804bd3…ddb2950f215fe1

1 in → 2 out46189.0340 XPM226 B

AMh4G9Sj…B7MepdJ4 ARhd3e8M…sQvcBCk4

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.

2.510 × 10⁹⁸(99-digit number)

25100285386247243411…67300374398237573119

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

2.510 × 10⁹⁸(99-digit number)

25100285386247243411…67300374398237573119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.510 × 10⁹⁸(99-digit number)

25100285386247243411…67300374398237573121

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

5.020 × 10⁹⁸(99-digit number)

50200570772494486823…34600748796475146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.020 × 10⁹⁸(99-digit number)

50200570772494486823…34600748796475146241

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

1.004 × 10⁹⁹(100-digit number)

10040114154498897364…69201497592950292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.004 × 10⁹⁹(100-digit number)

10040114154498897364…69201497592950292481

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

2.008 × 10⁹⁹(100-digit number)

20080228308997794729…38402995185900584959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.008 × 10⁹⁹(100-digit number)

20080228308997794729…38402995185900584961

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

4.016 × 10⁹⁹(100-digit number)

40160456617995589458…76805990371801169919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.016 × 10⁹⁹(100-digit number)

40160456617995589458…76805990371801169921

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 #2,177,896

Cookie Preferences