Block #290,481

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 5:27:56 PM · Difficulty 9.9892 · 6,527,532 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

866beba2a97b2e5196a0223db98c4479bf73f3d994836dfd0443386d796300a6

View on Chainz ↗

Height

#290,481

Difficulty

9.989231

Transactions

Size

1.76 KB

Version

Bits

09fd3e3c

Nonce

19,544

Timestamp

12/2/2013, 5:27:56 PM

Confirmations

6,527,532

Mined by

⛏️ P2SHALXVUbp1MjSbHewK9kyNzHHsYMsjywJoQi

Merkle Root

d6f8f8e335cbd7af0637977fae00661d32aad03e54c655696eac79056c0c8555

Transactions (5)

Coinbase0b245c52ded6fa…8474760e232758

1 in → 1 out10.0500 XPM109 B

ALXVUbp1…sjywJoQi

b994d1568e11c9…a481a5667c2172

3 in → 1 out1.0609 XPM487 B

AakCBgDN…KJzYPxJe

613fb085dbdec5…95cd92101fe116

1 in → 2 out4.8714 XPM226 B

Abv8pzf1…t4zPXDTV AYddHTtZ…zdZVWS9V

ee907405e0c281…09058d02d681b4

1 in → 2 out4.1236 XPM225 B

AXCprFwb…NtMz6VvL AK3jYrQf…AXnsVXJW

da0bb0dcdc73ca…7e27fdd05d0096

4 in → 2 out1.0255 XPM669 B

AaWZJEh6…xg8gB5gZ ANmNBEi1…tQe1uEZ8

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.

1.102 × 10⁹⁶(97-digit number)

11025994479240221872…89548642210242751439

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

1.102 × 10⁹⁶(97-digit number)

11025994479240221872…89548642210242751439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.102 × 10⁹⁶(97-digit number)

11025994479240221872…89548642210242751441

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

2.205 × 10⁹⁶(97-digit number)

22051988958480443744…79097284420485502879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.205 × 10⁹⁶(97-digit number)

22051988958480443744…79097284420485502881

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

4.410 × 10⁹⁶(97-digit number)

44103977916960887488…58194568840971005759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.410 × 10⁹⁶(97-digit number)

44103977916960887488…58194568840971005761

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

8.820 × 10⁹⁶(97-digit number)

88207955833921774977…16389137681942011519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.820 × 10⁹⁶(97-digit number)

88207955833921774977…16389137681942011521

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

1.764 × 10⁹⁷(98-digit number)

17641591166784354995…32778275363884023039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #290,481

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