Block #1,592,943

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/20/2016, 4:06:32 PM · Difficulty 10.6419 · 5,224,348 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bbdb3bc0c0517104027043ec6b9b07a13e69af617a36eafc510b2ff8f7efc7c7

View on Chainz ↗

Height

#1,592,943

Difficulty

10.641912

Transactions

Size

1.64 KB

Version

Bits

0aa45457

Nonce

339,326,226

Timestamp

5/20/2016, 4:06:32 PM

Confirmations

5,224,348

Mined by

⛏️ P2SHAU5SoXC4YVJrPb3CJCRhABeJG5ZjN5FvAq

Merkle Root

95ed71f61e6f0b44f6b038b8524c38fcc914b230f887508596a8cd14c4ec9ae3

Transactions (2)

Coinbase10293a895e0505…bbc54d39ccdd03

1 in → 1 out8.8400 XPM110 B

AU5SoXC4…ZjN5FvAq

ef799a22b29690…fd6faaecc3319d

1 in → 39 out96.1665 XPM1.45 KB

AHhsTm9d…4uzmG7tE AZb72Xpi…jMwjS9yX AG2zdSpG…Kqm47dPC ALoy71ky…9HsMoSuS AGmkxDJY…bhcdFUFZ

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.

9.931 × 10⁹⁴(95-digit number)

99318314055752550866…10986208531388411839

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

9.931 × 10⁹⁴(95-digit number)

99318314055752550866…10986208531388411839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.931 × 10⁹⁴(95-digit number)

99318314055752550866…10986208531388411841

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

1.986 × 10⁹⁵(96-digit number)

19863662811150510173…21972417062776823679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.986 × 10⁹⁵(96-digit number)

19863662811150510173…21972417062776823681

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

3.972 × 10⁹⁵(96-digit number)

39727325622301020346…43944834125553647359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.972 × 10⁹⁵(96-digit number)

39727325622301020346…43944834125553647361

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

7.945 × 10⁹⁵(96-digit number)

79454651244602040692…87889668251107294719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.945 × 10⁹⁵(96-digit number)

79454651244602040692…87889668251107294721

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

1.589 × 10⁹⁶(97-digit number)

15890930248920408138…75779336502214589439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.589 × 10⁹⁶(97-digit number)

15890930248920408138…75779336502214589441

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 #1,592,943

Cookie Preferences