Block #3,015,389

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/18/2019, 9:11:57 PM · Difficulty 11.1764 · 3,801,737 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d380b42bde8032d072d3d2dcd28e5711892d57eaa2fc9d8d5b33b446e49ed42d

View on Chainz ↗

Height

#3,015,389

Difficulty

11.176434

Transactions

Size

1.46 KB

Version

Bits

0b2d2ac0

Nonce

318,973,653

Timestamp

1/18/2019, 9:11:57 PM

Confirmations

3,801,737

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

d08ac42940db1cf6c6b5402ee480d104be572acc15f954f32acd49a3df1f4337

Transactions (5)

Coinbased5cf32b06e14f5…14938f228cdd49

1 in → 1 out8.0300 XPM110 B

AUhjokok…k5m93PZR

a78d126866eac7…c10721949a1917

2 in → 2 out15.9700 XPM305 B

AXs7pq7u…J7LpPpX2 ATEy9cxL…LgviB6pF

43ba75c560b972…f846034b6dd96a

2 in → 2 out16.1100 XPM308 B

Aeb1d5GJ…SXdKc84K AG68p8Eo…NFPCjJrz

d96ef56c7d7717…ad8b300320ec46

2 in → 2 out15.9700 XPM307 B

AFspDL7p…6fDLiH6h AHaY23yt…YFhPoMNu

25e9ac6f12f19c…22cf2709b27823

2 in → 2 out11.9300 XPM375 B

AZwS7wqn…3TrNxHog AaHsEQd6…A22sKQ7o

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.

1.480 × 10⁹⁵(96-digit number)

14803768615169027008…58206744102821806079

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

1.480 × 10⁹⁵(96-digit number)

14803768615169027008…58206744102821806079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.480 × 10⁹⁵(96-digit number)

14803768615169027008…58206744102821806081

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

2.960 × 10⁹⁵(96-digit number)

29607537230338054016…16413488205643612159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.960 × 10⁹⁵(96-digit number)

29607537230338054016…16413488205643612161

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

5.921 × 10⁹⁵(96-digit number)

59215074460676108032…32826976411287224319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.921 × 10⁹⁵(96-digit number)

59215074460676108032…32826976411287224321

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

1.184 × 10⁹⁶(97-digit number)

11843014892135221606…65653952822574448639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.184 × 10⁹⁶(97-digit number)

11843014892135221606…65653952822574448641

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

2.368 × 10⁹⁶(97-digit number)

23686029784270443212…31307905645148897279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.368 × 10⁹⁶(97-digit number)

23686029784270443212…31307905645148897281

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

4.737 × 10⁹⁶(97-digit number)

47372059568540886425…62615811290297794559

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 #3,015,389

Cookie Preferences