Block #2,233,251

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/2/2017, 4:30:46 AM · Difficulty 10.9461 · 4,603,505 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa0a945ac1bcd8ecf91d52fd1df27ed3f47cf03a1a98dc7f0472c4cef22a4635

View on Chainz ↗

Height

#2,233,251

Difficulty

10.946125

Transactions

Size

2.00 KB

Version

Bits

0af23541

Nonce

669,515,625

Timestamp

8/2/2017, 4:30:46 AM

Confirmations

4,603,505

Mined by

⛏️ P2SHAM5ywyXAo26tCrRo2uELfZNrQ9qZ4oR1uZ

Merkle Root

2351776fc903f9ebdec8094ac1c0535321d92467c4254993d169f30f0b64f8ef

Transactions (2)

Coinbase5650c52a7688f4…aaac58de2eb9c5

1 in → 1 out8.3500 XPM109 B

AM5ywyXA…qZ4oR1uZ

a3b11f4f8cb7f1…664b6d794564a6

12 in → 2 out204.4594 XPM1.81 KB

AdMWv1kt…jSntHdVf AHNCdGo6…Gxshm5Xs

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.

2.860 × 10⁹³(94-digit number)

28606294930750401894…05549721667646516879

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

2.860 × 10⁹³(94-digit number)

28606294930750401894…05549721667646516879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.860 × 10⁹³(94-digit number)

28606294930750401894…05549721667646516881

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

5.721 × 10⁹³(94-digit number)

57212589861500803789…11099443335293033759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.721 × 10⁹³(94-digit number)

57212589861500803789…11099443335293033761

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

1.144 × 10⁹⁴(95-digit number)

11442517972300160757…22198886670586067519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.144 × 10⁹⁴(95-digit number)

11442517972300160757…22198886670586067521

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

2.288 × 10⁹⁴(95-digit number)

22885035944600321515…44397773341172135039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.288 × 10⁹⁴(95-digit number)

22885035944600321515…44397773341172135041

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

4.577 × 10⁹⁴(95-digit number)

45770071889200643031…88795546682344270079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.577 × 10⁹⁴(95-digit number)

45770071889200643031…88795546682344270081

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 #2,233,251

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