Block #72,932

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 2:59:43 AM · Difficulty 8.9945 · 6,741,903 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84b447120a9adc934c9269177f3431ec7f44214864b5ed723cf50c8ab5bc3810

View on Chainz ↗

Height

#72,932

Difficulty

8.994451

Transactions

Size

199 B

Version

Bits

08fe945c

Nonce

1,205

Timestamp

7/21/2013, 2:59:43 AM

Confirmations

6,741,903

Mined by

⛏️ P2SHAHGPtSCNuYeecmqUQuK4cLJv6iGESamBFW

Merkle Root

5717e3354f295216678a28bf989cb5e20fb23c8e16579dbdd06518896c7ae254

Transactions (1)

Coinbase5717e3354f2952…6518896c7ae254

1 in → 1 out12.3400 XPM110 B

AHGPtSCN…GESamBFW

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.

3.774 × 10⁹¹(92-digit number)

37744182611524761972…57147940917982415359

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

3.774 × 10⁹¹(92-digit number)

37744182611524761972…57147940917982415359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.774 × 10⁹¹(92-digit number)

37744182611524761972…57147940917982415361

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

7.548 × 10⁹¹(92-digit number)

75488365223049523945…14295881835964830719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.548 × 10⁹¹(92-digit number)

75488365223049523945…14295881835964830721

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

1.509 × 10⁹²(93-digit number)

15097673044609904789…28591763671929661439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.509 × 10⁹²(93-digit number)

15097673044609904789…28591763671929661441

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

3.019 × 10⁹²(93-digit number)

30195346089219809578…57183527343859322879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.019 × 10⁹²(93-digit number)

30195346089219809578…57183527343859322881

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

6.039 × 10⁹²(93-digit number)

60390692178439619156…14367054687718645759

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 #72,932

Cookie Preferences