Block #1,232,515

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/11/2015, 11:34:38 PM · Difficulty 10.7443 · 5,594,351 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8d1c10660e22ca84916d0de99eef905f577145b75aab257b17f4f661e64e22b

View on Chainz ↗

Height

#1,232,515

Difficulty

10.744265

Transactions

Size

885 B

Version

Bits

0abe8821

Nonce

125,327,071

Timestamp

9/11/2015, 11:34:38 PM

Confirmations

5,594,351

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

f312923d030295e99c8829a8b239ef79ea178e8e0d0ca33f411bea4c5ec94a54

Transactions (4)

Coinbaseaaf8fb5fe74c70…9b24a5cc91c5ae

1 in → 1 out8.6800 XPM116 B

AJCEY9yy…tg97E6zm

fb663f27b6993a…4498a4f5669f11

1 in → 2 out48.8915 XPM225 B

AKsebF9o…26T4a6vn Ae9QhM1z…FJiaizyp

568dc874d206b7…f3060d86743c37

1 in → 2 out48.6560 XPM226 B

AMvALC7R…XWFDbk5g AS28PxYq…i6RuNYWs

305cc4d503ca2e…1ad2457a6d9b4c

1 in → 2 out16.7321 XPM226 B

Acrr7kJf…cnbxB5zr ALZpvgtC…LhjQg3LF

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.

3.536 × 10⁹⁸(99-digit number)

35364792389824797660…17115600627078574079

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

3.536 × 10⁹⁸(99-digit number)

35364792389824797660…17115600627078574079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.536 × 10⁹⁸(99-digit number)

35364792389824797660…17115600627078574081

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

7.072 × 10⁹⁸(99-digit number)

70729584779649595320…34231201254157148159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.072 × 10⁹⁸(99-digit number)

70729584779649595320…34231201254157148161

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

1.414 × 10⁹⁹(100-digit number)

14145916955929919064…68462402508314296319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.414 × 10⁹⁹(100-digit number)

14145916955929919064…68462402508314296321

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

2.829 × 10⁹⁹(100-digit number)

28291833911859838128…36924805016628592639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.829 × 10⁹⁹(100-digit number)

28291833911859838128…36924805016628592641

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

5.658 × 10⁹⁹(100-digit number)

56583667823719676256…73849610033257185279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.658 × 10⁹⁹(100-digit number)

56583667823719676256…73849610033257185281

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 #1,232,515

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