Block #3,013,010

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/17/2019, 5:39:31 AM · Difficulty 11.1746 · 3,803,324 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe19854f6f89579cd33e2dce8b0c78285580c83d1afd77e22cb21cdcb55a76a6

View on Chainz ↗

Height

#3,013,010

Difficulty

11.174634

Transactions

Size

1.30 KB

Version

Bits

0b2cb4d4

Nonce

15,873,184

Timestamp

1/17/2019, 5:39:31 AM

Confirmations

3,803,324

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

ad4a4fba6cbfd5bca7b795322883e3764074cf5b092737688923a6c4cdb8e56e

Transactions (4)

Coinbaseb8bf7f65aae623…afcf3acf81cd90

1 in → 1 out8.0300 XPM109 B

AUMQRepm…tAfKmdW1

25821b6b2a89d6…7bef6ba81b02ee

2 in → 2 out15.9100 XPM306 B

AZrrkiXx…HEKyFuAh AVxPhgnC…EZaDT7qy

eb966bd8c70699…c3ea317eeb2d9f

2 in → 2 out13.8600 XPM342 B

AaHsEQd6…A22sKQ7o AbrQdrZX…4ygqu2YM

b59a8f1f46fcd6…dab7323013ad38

3 in → 2 out10.4100 XPM487 B

ALNJmyqf…SXU2LZL7 ANiRSGwW…LtXULkMk

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.

1.858 × 10⁹⁷(98-digit number)

18580672656060709418…93610309211728445439

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

1.858 × 10⁹⁷(98-digit number)

18580672656060709418…93610309211728445439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.858 × 10⁹⁷(98-digit number)

18580672656060709418…93610309211728445441

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

3.716 × 10⁹⁷(98-digit number)

37161345312121418836…87220618423456890879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.716 × 10⁹⁷(98-digit number)

37161345312121418836…87220618423456890881

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

7.432 × 10⁹⁷(98-digit number)

74322690624242837673…74441236846913781759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.432 × 10⁹⁷(98-digit number)

74322690624242837673…74441236846913781761

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

1.486 × 10⁹⁸(99-digit number)

14864538124848567534…48882473693827563519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.486 × 10⁹⁸(99-digit number)

14864538124848567534…48882473693827563521

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

2.972 × 10⁹⁸(99-digit number)

29729076249697135069…97764947387655127039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.972 × 10⁹⁸(99-digit number)

29729076249697135069…97764947387655127041

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

5.945 × 10⁹⁸(99-digit number)

59458152499394270138…95529894775310254079

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 #3,013,010

Cookie Preferences