Block #81,989

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 3:28:26 AM · Difficulty 9.2702 · 6,728,842 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

25c388b2e71590819aa6a592d1e547e8dad82ce550cbbeb7e4480bec02e470b9

View on Chainz ↗

Height

#81,989

Difficulty

9.270224

Transactions

Size

361 B

Version

Bits

09452d68

Nonce

291

Timestamp

7/25/2013, 3:28:26 AM

Confirmations

6,728,842

Mined by

⛏️ P2SHAZu9TuEFcCyZNNLXeTfQuTu7jYRkLBJ4RL

Merkle Root

19e9264c13a74c69c48e3f59d04284ae6267e696400f7e83ffe3f7ea3d1075d3

Transactions (2)

Coinbase1c3ddfe9d68bfe…695b7881a4c560

1 in → 1 out11.6300 XPM110 B

AZu9TuEF…RkLBJ4RL

a32858dec52dc0…c091a029d7ea15

1 in → 1 out11.7100 XPM157 B

AVXpXMS3…dbsyn72W

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.

3.142 × 10¹⁰⁵(106-digit number)

31428618078274360353…37239244832439546949

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

3.142 × 10¹⁰⁵(106-digit number)

31428618078274360353…37239244832439546949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.142 × 10¹⁰⁵(106-digit number)

31428618078274360353…37239244832439546951

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

6.285 × 10¹⁰⁵(106-digit number)

62857236156548720707…74478489664879093899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.285 × 10¹⁰⁵(106-digit number)

62857236156548720707…74478489664879093901

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

1.257 × 10¹⁰⁶(107-digit number)

12571447231309744141…48956979329758187799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.257 × 10¹⁰⁶(107-digit number)

12571447231309744141…48956979329758187801

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

2.514 × 10¹⁰⁶(107-digit number)

25142894462619488282…97913958659516375599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.514 × 10¹⁰⁶(107-digit number)

25142894462619488282…97913958659516375601

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

5.028 × 10¹⁰⁶(107-digit number)

50285788925238976565…95827917319032751199

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 #81,989

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