Block #1,301,444

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/27/2015, 6:02:14 PM · Difficulty 10.8614 · 5,523,119 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c55794c0a3988008b4e7c5684f7f606027a16a9db86929e5d52effb927d74151

View on Chainz ↗

Height

#1,301,444

Difficulty

10.861352

Transactions

Size

968 B

Version

Bits

0adc8190

Nonce

934,727,689

Timestamp

10/27/2015, 6:02:14 PM

Confirmations

5,523,119

Mined by

⛏️ P2SHAYiASwHWMyW3SXtEE8EYHvKQANYRG4VdrK

Merkle Root

662e2d3bf126fc40edf0997eca1bbb177f90423f152143d4e5e1aa48106c52e1

Transactions (2)

Coinbased571cc80f85453…89e1e5cef6d1e0

1 in → 1 out8.4700 XPM110 B

AYiASwHW…YRG4VdrK

a9ff2f29567ead…3bc01c64358fd0

1 in → 18 out103.3671 XPM769 B

AQJ44PSB…bq4A22yP AdEb8Jj7…fYCYHo7M AHKsvrsX…niSCYCkF AV5gWt6L…FZWcoxdh AWn91uFa…CooACLLm

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.

1.787 × 10⁹²(93-digit number)

17875240212921095413…79506396459905208719

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

1.787 × 10⁹²(93-digit number)

17875240212921095413…79506396459905208719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.787 × 10⁹²(93-digit number)

17875240212921095413…79506396459905208721

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

3.575 × 10⁹²(93-digit number)

35750480425842190827…59012792919810417439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.575 × 10⁹²(93-digit number)

35750480425842190827…59012792919810417441

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

7.150 × 10⁹²(93-digit number)

71500960851684381654…18025585839620834879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.150 × 10⁹²(93-digit number)

71500960851684381654…18025585839620834881

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

1.430 × 10⁹³(94-digit number)

14300192170336876330…36051171679241669759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.430 × 10⁹³(94-digit number)

14300192170336876330…36051171679241669761

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

2.860 × 10⁹³(94-digit number)

28600384340673752661…72102343358483339519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.860 × 10⁹³(94-digit number)

28600384340673752661…72102343358483339521

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 #1,301,444

Cookie Preferences