Block #59,051

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 12:06:35 AM · Difficulty 8.9630 · 6,748,866 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92162523ed1d14d6520e3a53cf41330236c6b81a1ac6269096d0c9f9289eabb4

View on Chainz ↗

Height

#59,051

Difficulty

8.963033

Transactions

Size

207 B

Version

Bits

08f68957

Nonce

246

Timestamp

7/18/2013, 12:06:35 AM

Confirmations

6,748,866

Mined by

⛏️ P2SHALQe3szxRuneHLtnSry8FnK36VpuoDtc9Z

Merkle Root

50b234272bd8d626a6d43746c04fdc95cf35eb4daf213addb9f5b4b0fd260313

Transactions (1)

Coinbase50b234272bd8d6…f5b4b0fd260313

1 in → 1 out12.4300 XPM110 B

ALQe3szx…puoDtc9Z

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.

4.061 × 10¹¹¹(112-digit number)

40612276916793403181…07555858032180134599

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

4.061 × 10¹¹¹(112-digit number)

40612276916793403181…07555858032180134599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.061 × 10¹¹¹(112-digit number)

40612276916793403181…07555858032180134601

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

8.122 × 10¹¹¹(112-digit number)

81224553833586806363…15111716064360269199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.122 × 10¹¹¹(112-digit number)

81224553833586806363…15111716064360269201

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

1.624 × 10¹¹²(113-digit number)

16244910766717361272…30223432128720538399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.624 × 10¹¹²(113-digit number)

16244910766717361272…30223432128720538401

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

3.248 × 10¹¹²(113-digit number)

32489821533434722545…60446864257441076799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.248 × 10¹¹²(113-digit number)

32489821533434722545…60446864257441076801

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

6.497 × 10¹¹²(113-digit number)

64979643066869445090…20893728514882153599

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 #59,051

Cookie Preferences