Block #489,230

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 4:31:41 AM · Difficulty 10.6622 · 6,320,951 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f11f3a7f00630c03b8b34ba7f4bfa4085649aef037fe10c2ee52030a513bec3f

View on Chainz ↗

Height

#489,230

Difficulty

10.662214

Transactions

Size

708 B

Version

Bits

0aa986d6

Nonce

258,156

Timestamp

4/13/2014, 4:31:41 AM

Confirmations

6,320,951

Mined by

⛏️ wMAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

037b5123bcc261b4841266c80fc5d6ba858da7f1980c999380a26290ea69f8e9

Transactions (3)

Coinbase63899c5eb00ad0…10bc553836e07d

1 in → 3 out8.8000 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

439e12fa1ff8bd…58eafe39e32b3a

1 in → 2 out3.7721 XPM226 B

Ab3ZA77H…R7ktRp2N AdeeajEM…CKSjA4CS

bc7d043298f4a6…941b807033977e

1 in → 2 out4.8190 XPM227 B

AcGZebaj…BcX1msWw AcQfxVUD…vQnNph4X

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.

7.748 × 10⁹³(94-digit number)

77483520784080255578…47505491732603944959

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

7.748 × 10⁹³(94-digit number)

77483520784080255578…47505491732603944959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.748 × 10⁹³(94-digit number)

77483520784080255578…47505491732603944961

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

1.549 × 10⁹⁴(95-digit number)

15496704156816051115…95010983465207889919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.549 × 10⁹⁴(95-digit number)

15496704156816051115…95010983465207889921

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

3.099 × 10⁹⁴(95-digit number)

30993408313632102231…90021966930415779839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.099 × 10⁹⁴(95-digit number)

30993408313632102231…90021966930415779841

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

6.198 × 10⁹⁴(95-digit number)

61986816627264204462…80043933860831559679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.198 × 10⁹⁴(95-digit number)

61986816627264204462…80043933860831559681

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

1.239 × 10⁹⁵(96-digit number)

12397363325452840892…60087867721663119359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.239 × 10⁹⁵(96-digit number)

12397363325452840892…60087867721663119361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #489,230

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