Block #2,821,430

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/2/2018, 1:49:11 PM · Difficulty 11.7019 · 4,022,610 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24beadf456356dff7981745aa90a708760909e0d5ddb2b32721f054d618fc5d5

View on Chainz ↗

Height

#2,821,430

Difficulty

11.701861

Transactions

Size

1.93 KB

Version

Bits

0bb3ad30

Nonce

1,030,278,155

Timestamp

9/2/2018, 1:49:11 PM

Confirmations

4,022,610

Mined by

⛏️ P2SHAcXu9uPZKyuCY5jPcf4E78rU6JaNdLusCj

Merkle Root

6fbb6fd7fd2daa6d613efbb4df9146464c2d5efec44182d3022d19fd25e0cb5f

Transactions (5)

Coinbasec575182075223c…41f70bd9f95385

1 in → 1 out7.3300 XPM110 B

AcXu9uPZ…aNdLusCj

c900bb1a945ce7…1a90eec200cc36

5 in → 2 out36.5600 XPM650 B

AHnrKgTh…XWqX7yNa AW4vm7K2…CyKApbJi

f5d8bdb3342f81…2162f31954bffe

1 in → 2 out5.7474 XPM226 B

AHAcb3sF…eH6jxgYM ARDAecnL…Wyec8Fxe

3a84a6b8ba112f…39e83e9a16dee7

1 in → 2 out4.5481 XPM225 B

AbNpfvTG…b4gH6xLW AWLhispt…YegP97ro

4135a74a0967f0…221359507703b2

4 in → 2 out4.0175 XPM671 B

AYny1ZKx…nmyLGavN ANuKDHaq…8xtWLJ56

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.

2.802 × 10⁹⁷(98-digit number)

28026994030649220254…45692460944213934079

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

2.802 × 10⁹⁷(98-digit number)

28026994030649220254…45692460944213934079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.802 × 10⁹⁷(98-digit number)

28026994030649220254…45692460944213934081

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

5.605 × 10⁹⁷(98-digit number)

56053988061298440508…91384921888427868159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.605 × 10⁹⁷(98-digit number)

56053988061298440508…91384921888427868161

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

1.121 × 10⁹⁸(99-digit number)

11210797612259688101…82769843776855736319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.121 × 10⁹⁸(99-digit number)

11210797612259688101…82769843776855736321

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

2.242 × 10⁹⁸(99-digit number)

22421595224519376203…65539687553711472639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.242 × 10⁹⁸(99-digit number)

22421595224519376203…65539687553711472641

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

4.484 × 10⁹⁸(99-digit number)

44843190449038752406…31079375107422945279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.484 × 10⁹⁸(99-digit number)

44843190449038752406…31079375107422945281

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

8.968 × 10⁹⁸(99-digit number)

89686380898077504813…62158750214845890559

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 #2,821,430

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