Block #1,112,320

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/17/2015, 6:23:45 AM · Difficulty 10.8945 · 5,702,784 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

56400aa559ef90161e75f5344e1f2bf6d2c3aaf296a30dd3116a3fec6f82ff06

View on Chainz ↗

Height

#1,112,320

Difficulty

10.894476

Transactions

Size

16.17 KB

Version

Bits

0ae4fc5c

Nonce

88,091,973

Timestamp

6/17/2015, 6:23:45 AM

Confirmations

5,702,784

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

8e716afb054f744bd793c1afb2f7e2967cc25b250b7e05458058311eb519c712

Transactions (4)

Coinbased4f118d20d1d17…f5330f3e0af15b

1 in → 1 out8.6300 XPM116 B

AJCEY9yy…tg97E6zm

6a07267d416a37…6dfc7200b04eed

1 in → 2 out1925.9900 XPM225 B

APxphXQH…Ag8KQAWS AYAaDUEJ…dxhJdmZz

70eea6d11bacbe…8c777d2d5085ba

1 in → 2 out815.3762 XPM226 B

AQHE5e6H…xDwU3vYU AJ822sjS…3xDM1d3c

c87f11fbc517db…628c9fb22ba8f7

107 in → 2 out75.0000 XPM15.53 KB

AQ7jd3sV…fT6uK9gu AJySnNqu…3adXwvuc

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.

8.568 × 10⁹⁷(98-digit number)

85680731612815999288…02179219410637276159

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

8.568 × 10⁹⁷(98-digit number)

85680731612815999288…02179219410637276159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.568 × 10⁹⁷(98-digit number)

85680731612815999288…02179219410637276161

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

1.713 × 10⁹⁸(99-digit number)

17136146322563199857…04358438821274552319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.713 × 10⁹⁸(99-digit number)

17136146322563199857…04358438821274552321

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

3.427 × 10⁹⁸(99-digit number)

34272292645126399715…08716877642549104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.427 × 10⁹⁸(99-digit number)

34272292645126399715…08716877642549104641

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

6.854 × 10⁹⁸(99-digit number)

68544585290252799430…17433755285098209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.854 × 10⁹⁸(99-digit number)

68544585290252799430…17433755285098209281

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

1.370 × 10⁹⁹(100-digit number)

13708917058050559886…34867510570196418559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.370 × 10⁹⁹(100-digit number)

13708917058050559886…34867510570196418561

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 #1,112,320

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