Block #2,158,422

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/13/2017, 1:38:06 AM · Difficulty 10.9052 · 4,667,900 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

132f6a5db6c7e58f0ddf10cae32ced82476ac50d5ed69400ce791a937085ce2d

View on Chainz ↗

Height

#2,158,422

Difficulty

10.905189

Transactions

Size

2.04 KB

Version

Bits

0ae7ba70

Nonce

302,330,956

Timestamp

6/13/2017, 1:38:06 AM

Confirmations

4,667,900

Mined by

⛏️ P2SHAKwHYnjk7BoZtS39H9uA3dMtz46diDiNU3

Merkle Root

890d1ca9d49ec752ffdd5dc4dcae288463d780feb2737ee0cd4d0db742cc52e3

Transactions (2)

Coinbase37e4ed1beaff52…eada1320a37d66

1 in → 1 out8.4800 XPM109 B

AKwHYnjk…6diDiNU3

1ee0f0d2cdc86e…c128c9cfe2f3a9

12 in → 3 out2763.5706 XPM1.85 KB

AdHUmmiC…9mN628aD AUYuXW7N…boKeDr2Y AcBaooYt…xSomgUCF

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.

3.831 × 10⁹⁶(97-digit number)

38317806215962625210…11541793093673328639

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

3.831 × 10⁹⁶(97-digit number)

38317806215962625210…11541793093673328639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.831 × 10⁹⁶(97-digit number)

38317806215962625210…11541793093673328641

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

7.663 × 10⁹⁶(97-digit number)

76635612431925250421…23083586187346657279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.663 × 10⁹⁶(97-digit number)

76635612431925250421…23083586187346657281

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

1.532 × 10⁹⁷(98-digit number)

15327122486385050084…46167172374693314559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.532 × 10⁹⁷(98-digit number)

15327122486385050084…46167172374693314561

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

3.065 × 10⁹⁷(98-digit number)

30654244972770100168…92334344749386629119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.065 × 10⁹⁷(98-digit number)

30654244972770100168…92334344749386629121

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

6.130 × 10⁹⁷(98-digit number)

61308489945540200337…84668689498773258239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.130 × 10⁹⁷(98-digit number)

61308489945540200337…84668689498773258241

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 #2,158,422

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