Block #489,987

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 2:44:16 PM · Difficulty 10.6719 · 6,305,346 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7051cc4deb19be73653abfc7feaac40bfb633773c99e206f893a3e10901ba78

View on Chainz ↗

Height

#489,987

Difficulty

10.671886

Transactions

Size

1.09 KB

Version

Bits

0aac00bc

Nonce

124,015,470

Timestamp

4/13/2014, 2:44:16 PM

Confirmations

6,305,346

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5b22cf5fae1775f25269f22f793b63b4c06449eb004aff56df134d014238adcd

Transactions (5)

Coinbase1f5c54f180e875…a968df61afbd74

1 in → 1 out8.8100 XPM116 B

AbwWkWZt…kawDhufa

213f7a55d83513…3a4b8bcab64995

1 in → 2 out6.7906 XPM225 B

AQYh3Vj9…jwkpgczw AGnzYQwo…HnuYVFGs

12eae4ed06d7f9…7d1172742d0f83

1 in → 2 out2.7785 XPM226 B

AdEbjus7…e8HE2UWp AccMHKyd…Pdy71zpV

4713db3a497019…c72e90a715d336

1 in → 2 out6.7956 XPM227 B

AGxMeQpn…PtE4vAxN AHKr7yvB…JFtRTr2m

54f080a3a4b702…f19a8f1fbd4f2a

1 in → 2 out6.7901 XPM227 B

AY7WXfK3…WQDMHqf8 AWKABGNT…S8EdENHa

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.

2.938 × 10⁹⁷(98-digit number)

29382552383448656086…75975086987884491339

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

2.938 × 10⁹⁷(98-digit number)

29382552383448656086…75975086987884491339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.938 × 10⁹⁷(98-digit number)

29382552383448656086…75975086987884491341

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

5.876 × 10⁹⁷(98-digit number)

58765104766897312172…51950173975768982679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.876 × 10⁹⁷(98-digit number)

58765104766897312172…51950173975768982681

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

1.175 × 10⁹⁸(99-digit number)

11753020953379462434…03900347951537965359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.175 × 10⁹⁸(99-digit number)

11753020953379462434…03900347951537965361

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

2.350 × 10⁹⁸(99-digit number)

23506041906758924869…07800695903075930719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.350 × 10⁹⁸(99-digit number)

23506041906758924869…07800695903075930721

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

4.701 × 10⁹⁸(99-digit number)

47012083813517849738…15601391806151861439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.701 × 10⁹⁸(99-digit number)

47012083813517849738…15601391806151861441

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