Block #3,060,426

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/20/2019, 12:22:07 AM · Difficulty 11.0114 · 3,783,032 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a68d93cc4c68ffc8ad44ce34bee1d12e3e99a6086d3f5fca24cbe72807519f6a

View on Chainz ↗

Height

#3,060,426

Difficulty

11.011390

Transactions

Size

653 B

Version

Bits

0b02ea78

Nonce

1,110,854,065

Timestamp

2/20/2019, 12:22:07 AM

Confirmations

3,783,032

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

85e26ca2b2dae82077cb9f9966114511f76f6b222846588d78d6e6c586093f31

Transactions (3)

Coinbase93525b7e75446c…ea06f6a825c8f8

1 in → 1 out8.2500 XPM110 B

AUMQRepm…tAfKmdW1

a623f92f31ac5d…221d1092665827

1 in → 2 out4.2152 XPM226 B

AbXwmGxD…4XXYP765 AHfFvMTb…vwrRHALW

9ca9c614cca0fa…fc424c0928cf06

1 in → 2 out1.4439 XPM226 B

AbXwmGxD…4XXYP765 AP21FpxC…ntAWgp39

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.

2.541 × 10⁹⁷(98-digit number)

25410506296642067793…06307823414529474559

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

2.541 × 10⁹⁷(98-digit number)

25410506296642067793…06307823414529474559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.541 × 10⁹⁷(98-digit number)

25410506296642067793…06307823414529474561

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

5.082 × 10⁹⁷(98-digit number)

50821012593284135586…12615646829058949119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.082 × 10⁹⁷(98-digit number)

50821012593284135586…12615646829058949121

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

1.016 × 10⁹⁸(99-digit number)

10164202518656827117…25231293658117898239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.016 × 10⁹⁸(99-digit number)

10164202518656827117…25231293658117898241

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

2.032 × 10⁹⁸(99-digit number)

20328405037313654234…50462587316235796479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.032 × 10⁹⁸(99-digit number)

20328405037313654234…50462587316235796481

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

4.065 × 10⁹⁸(99-digit number)

40656810074627308468…00925174632471592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.065 × 10⁹⁸(99-digit number)

40656810074627308468…00925174632471592961

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

8.131 × 10⁹⁸(99-digit number)

81313620149254616937…01850349264943185919

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 #3,060,426

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