Block #1,195,245

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/15/2015, 11:50:36 AM · Difficulty 10.8375 · 5,621,913 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72b2bd29c996dd3f5a29b3c189beb9559bc993fdfbce476578e4681f6e37e23d

View on Chainz ↗

Height

#1,195,245

Difficulty

10.837535

Transactions

Size

426 B

Version

Bits

0ad668ab

Nonce

1,183,652,424

Timestamp

8/15/2015, 11:50:36 AM

Confirmations

5,621,913

Mined by

⛏️ P2SHAazJuV8m86CAmTwdUWJTTti7ei5Vmibmoq

Merkle Root

db986ffc48dad6d2c8f60b42530012a151160fa2e8bafa74fb2ec443ae1f2720

Transactions (2)

Coinbase776d67f56c11df…bb7f02375f1e39

1 in → 1 out8.5100 XPM110 B

AazJuV8m…5Vmibmoq

303a09743f501d…6cd908696c6321

1 in → 2 out0.1320 XPM226 B

AVrmLMRU…EPfdLtuA AamSff8f…gETREVvZ

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.

2.231 × 10⁹⁵(96-digit number)

22319976518110104178…58175352397785292159

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

2.231 × 10⁹⁵(96-digit number)

22319976518110104178…58175352397785292159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.231 × 10⁹⁵(96-digit number)

22319976518110104178…58175352397785292161

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

4.463 × 10⁹⁵(96-digit number)

44639953036220208356…16350704795570584319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.463 × 10⁹⁵(96-digit number)

44639953036220208356…16350704795570584321

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

8.927 × 10⁹⁵(96-digit number)

89279906072440416713…32701409591141168639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.927 × 10⁹⁵(96-digit number)

89279906072440416713…32701409591141168641

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

1.785 × 10⁹⁶(97-digit number)

17855981214488083342…65402819182282337279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.785 × 10⁹⁶(97-digit number)

17855981214488083342…65402819182282337281

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

3.571 × 10⁹⁶(97-digit number)

35711962428976166685…30805638364564674559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.571 × 10⁹⁶(97-digit number)

35711962428976166685…30805638364564674561

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 #1,195,245

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