Block #2,316,328

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/30/2017, 9:07:34 PM · Difficulty 10.9090 · 4,522,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4d0357c202e764618de5992fe7181514853ce04e90bcf3b8df1c0773ff8ccf84

View on Chainz ↗

Height

#2,316,328

Difficulty

10.909023

Transactions

Size

46.12 KB

Version

Bits

0ae8b5bf

Nonce

409,842,007

Timestamp

9/30/2017, 9:07:34 PM

Confirmations

4,522,248

Mined by

⛏️ P2SHAe3Ug7pvThcAQYmmjVHyxbzGu61mZmnU2g

Merkle Root

233c7531c9f99efc8d6ff291e4517dd971def2a9dff6c49fa6f558a348e77ce9

Transactions (2)

Coinbase14901affbec75f…80f4b36625998f

1 in → 1 out8.8700 XPM109 B

Ae3Ug7pv…1mZmnU2g

6185af6dbb3ce8…6d587d2fc24bd1

412 in → 2 out3436.4000 XPM45.92 KB

AZF8nuUQ…kNgS9cHy APYjX3jo…ikPzpHdt

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.

6.916 × 10⁹⁸(99-digit number)

69166661198494100222…88811739640129454079

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

6.916 × 10⁹⁸(99-digit number)

69166661198494100222…88811739640129454079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.916 × 10⁹⁸(99-digit number)

69166661198494100222…88811739640129454081

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

1.383 × 10⁹⁹(100-digit number)

13833332239698820044…77623479280258908159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.383 × 10⁹⁹(100-digit number)

13833332239698820044…77623479280258908161

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

2.766 × 10⁹⁹(100-digit number)

27666664479397640088…55246958560517816319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.766 × 10⁹⁹(100-digit number)

27666664479397640088…55246958560517816321

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

5.533 × 10⁹⁹(100-digit number)

55333328958795280177…10493917121035632639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.533 × 10⁹⁹(100-digit number)

55333328958795280177…10493917121035632641

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

1.106 × 10¹⁰⁰(101-digit number)

11066665791759056035…20987834242071265279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.106 × 10¹⁰⁰(101-digit number)

11066665791759056035…20987834242071265281

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 #2,316,328

Cookie Preferences