Block #2,428,359

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/17/2017, 1:45:14 PM · Difficulty 10.9148 · 4,412,794 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5230c7224cf69c30cd8b6fcd2dc42380f472733d946c05bb9c3d50659935ee81

View on Chainz ↗

Height

#2,428,359

Difficulty

10.914818

Transactions

Size

1.18 KB

Version

Bits

0aea3187

Nonce

7,832,717

Timestamp

12/17/2017, 1:45:14 PM

Confirmations

4,412,794

Mined by

⛏️ P2SHARyc22hfmTXe1XKbPNPiEXQ461HR3bF1HU

Merkle Root

56e17c43c1a032d15a0684d77f61fefae6afd967ce2878e9bbdbd664908f962f

Transactions (3)

Coinbasebdf58242485d26…4cf7edaf8c8133

1 in → 1 out8.4000 XPM109 B

ARyc22hf…HR3bF1HU

626c257838ec36…5eeb5041ec103f

3 in → 2 out3461.3959 XPM521 B

AFnSLrR7…C7CCjj2C AbfHPQRP…cc1QCTYa

a260492f90ea83…05c7fbd446892b

3 in → 2 out10.3637 XPM489 B

AevxZoN3…fwTLU9Fn ANG9DZMb…Qy6fhggZ

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.

2.790 × 10⁹⁵(96-digit number)

27909817042441006192…64622952436568611839

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

2.790 × 10⁹⁵(96-digit number)

27909817042441006192…64622952436568611839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.790 × 10⁹⁵(96-digit number)

27909817042441006192…64622952436568611841

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

5.581 × 10⁹⁵(96-digit number)

55819634084882012385…29245904873137223679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.581 × 10⁹⁵(96-digit number)

55819634084882012385…29245904873137223681

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

1.116 × 10⁹⁶(97-digit number)

11163926816976402477…58491809746274447359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.116 × 10⁹⁶(97-digit number)

11163926816976402477…58491809746274447361

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

2.232 × 10⁹⁶(97-digit number)

22327853633952804954…16983619492548894719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.232 × 10⁹⁶(97-digit number)

22327853633952804954…16983619492548894721

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

4.465 × 10⁹⁶(97-digit number)

44655707267905609908…33967238985097789439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.465 × 10⁹⁶(97-digit number)

44655707267905609908…33967238985097789441

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

8.931 × 10⁹⁶(97-digit number)

89311414535811219817…67934477970195578879

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 #2,428,359

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