Block #3,030,489

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/29/2019, 3:29:36 PM · Difficulty 11.1087 · 3,785,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7690c02039c30673c24f5f04c3c32679cfc7cf8d6a476e2e643c4fd9bb380a0

View on Chainz ↗

Height

#3,030,489

Difficulty

11.108717

Transactions

Size

1.33 KB

Version

Bits

0b1bd4e1

Nonce

424,417,200

Timestamp

1/29/2019, 3:29:36 PM

Confirmations

3,785,571

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

35ceec85a3e87fd6b7cf22c9a0f7fa5dbd2e1602834556141baa8f44d94187a0

Transactions (3)

Coinbase06f27f9939d57b…336413ea80e6ed

1 in → 1 out8.1100 XPM109 B

AbXwmGxD…4XXYP765

872fadc6d06872…cf87888282be72

5 in → 2 out183.6070 XPM818 B

AYd8oFLh…gsLSYeTc AUMAFvFG…U3tviQiX

b965c9aebc7abc…b33b9d5b272087

2 in → 2 out10.0600 XPM339 B

Aeb1d5GJ…SXdKc84K AcKxvRzc…doduTDxL

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.

8.576 × 10⁹⁶(97-digit number)

85768119285383114941…45023189936962887679

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

8.576 × 10⁹⁶(97-digit number)

85768119285383114941…45023189936962887679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.576 × 10⁹⁶(97-digit number)

85768119285383114941…45023189936962887681

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

1.715 × 10⁹⁷(98-digit number)

17153623857076622988…90046379873925775359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.715 × 10⁹⁷(98-digit number)

17153623857076622988…90046379873925775361

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

3.430 × 10⁹⁷(98-digit number)

34307247714153245976…80092759747851550719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.430 × 10⁹⁷(98-digit number)

34307247714153245976…80092759747851550721

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

6.861 × 10⁹⁷(98-digit number)

68614495428306491953…60185519495703101439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.861 × 10⁹⁷(98-digit number)

68614495428306491953…60185519495703101441

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

1.372 × 10⁹⁸(99-digit number)

13722899085661298390…20371038991406202879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.372 × 10⁹⁸(99-digit number)

13722899085661298390…20371038991406202881

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

2.744 × 10⁹⁸(99-digit number)

27445798171322596781…40742077982812405759

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 #3,030,489

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