Block #989,915

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/25/2015, 9:10:55 AM · Difficulty 10.8522 · 5,802,780 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5d67d1543880bdd61291b35f0617cb44e26266a4cb7ee214371b8a32b9c5d1f

View on Chainz ↗

Height

#989,915

Difficulty

10.852220

Transactions

Size

3.82 KB

Version

Bits

0ada2b1b

Nonce

1,943,384,524

Timestamp

3/25/2015, 9:10:55 AM

Confirmations

5,802,780

Merkle Root

70206cf66cf9fc2371ec6f44ef79539d4493473bee45362ed1bd57c97d97b329

Transactions (5)

Coinbasebe2eb0ef10d18f…41d93e8fcad885

1 in → 1 out8.5400 XPM110 B

AGq88FoV…FJqL8htT

8beaa80ea86801…734579a4deeaf4

16 in → 2 out12488.6100 XPM2.39 KB

AYSmH4d7…237QEFqX ARpjHv1k…4F9NvuWN

d36691ae254f96…e68680f71f2b99

4 in → 2 out31.7155 XPM668 B

AHZkUHtR…EUjZu7Tf AeU6hrZv…Cj4EAcXs

fe3b1d1db80ff8…6f9995188c25ee

2 in → 2 out15.8860 XPM375 B

Af2928xo…zQPGi7fn AdUwqsJC…kyCDagPM

53eecc5d921a77…7a38e84f007003

1 in → 2 out7.1983 XPM225 B

Af3aPj7K…cnGd5dnY AK1xJ4NW…mQaTFVE8

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.

3.703 × 10⁹⁶(97-digit number)

37034766468653031901…71338418964245381119

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

3.703 × 10⁹⁶(97-digit number)

37034766468653031901…71338418964245381119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.703 × 10⁹⁶(97-digit number)

37034766468653031901…71338418964245381121

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

7.406 × 10⁹⁶(97-digit number)

74069532937306063802…42676837928490762239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.406 × 10⁹⁶(97-digit number)

74069532937306063802…42676837928490762241

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

1.481 × 10⁹⁷(98-digit number)

14813906587461212760…85353675856981524479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.481 × 10⁹⁷(98-digit number)

14813906587461212760…85353675856981524481

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

2.962 × 10⁹⁷(98-digit number)

29627813174922425520…70707351713963048959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.962 × 10⁹⁷(98-digit number)

29627813174922425520…70707351713963048961

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

5.925 × 10⁹⁷(98-digit number)

59255626349844851041…41414703427926097919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.925 × 10⁹⁷(98-digit number)

59255626349844851041…41414703427926097921

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