Block #3,011,049

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/15/2019, 6:36:12 PM · Difficulty 11.1974 · 3,827,746 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7299a855497d09313c7080dd2b59a469ae11eee1375adb3f9260d529cf3e2d39

View on Chainz ↗

Height

#3,011,049

Difficulty

11.197449

Transactions

Size

1.17 KB

Version

Bits

0b328c00

Nonce

610,878,325

Timestamp

1/15/2019, 6:36:12 PM

Confirmations

3,827,746

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

d9d5351d97604de8824e968aab70bb84b5d3547c6121e83b98f0e28fa3696b71

Transactions (5)

Coinbase7254067f9779e9…34548dd49afc9e

1 in → 1 out8.0000 XPM110 B

AUMQRepm…tAfKmdW1

57ccea2315d1f6…67bdeb197d4353

3 in → 2 out23.8400 XPM420 B

AemY4Zt4…87UF1iHf AUhjokok…k5m93PZR

3c62caa2e9b691…e50c22c18680a5

1 in → 2 out7.9400 XPM191 B

AXh8UBXr…JUzAfddX AUhjokok…k5m93PZR

c956d575ee74f4…a309c00b9fc34d

1 in → 2 out7.9400 XPM193 B

AUhjokok…k5m93PZR AeF5bhdp…7KFt4mPQ

524c79796ea846…df63d557794ea2

1 in → 2 out7.9400 XPM192 B

AUhjokok…k5m93PZR Ae8vJNTs…e3Rdrbxf

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.

4.122 × 10⁹⁵(96-digit number)

41225565226881837144…73322776923822157439

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

4.122 × 10⁹⁵(96-digit number)

41225565226881837144…73322776923822157439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.122 × 10⁹⁵(96-digit number)

41225565226881837144…73322776923822157441

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

8.245 × 10⁹⁵(96-digit number)

82451130453763674288…46645553847644314879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.245 × 10⁹⁵(96-digit number)

82451130453763674288…46645553847644314881

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

1.649 × 10⁹⁶(97-digit number)

16490226090752734857…93291107695288629759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.649 × 10⁹⁶(97-digit number)

16490226090752734857…93291107695288629761

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

3.298 × 10⁹⁶(97-digit number)

32980452181505469715…86582215390577259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.298 × 10⁹⁶(97-digit number)

32980452181505469715…86582215390577259521

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

6.596 × 10⁹⁶(97-digit number)

65960904363010939430…73164430781154519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.596 × 10⁹⁶(97-digit number)

65960904363010939430…73164430781154519041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.319 × 10⁹⁷(98-digit number)

13192180872602187886…46328861562309038079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #3,011,049

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