Block #1,628,812

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/14/2016, 11:14:39 PM · Difficulty 10.6015 · 5,187,395 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

252f16458df1f813af8a045e7653c5c115b538e7be88dbcea977a10af99d3aec

View on Chainz ↗

Height

#1,628,812

Difficulty

10.601478

Transactions

Size

17.58 KB

Version

Bits

0a99fa74

Nonce

1,559,217,917

Timestamp

6/14/2016, 11:14:39 PM

Confirmations

5,187,395

Mined by

⛏️ P2SHAbV5EM7dvUFJdhjH1teWuVusxFm2B5tjYk

Merkle Root

2450c82a2259412bc3396ecbe9b895a6f6be72fc981d02c027aa955298b00ddf

Transactions (4)

Coinbase710ad34fdef40e…c84cab75e0f276

1 in → 1 out9.0800 XPM109 B

AbV5EM7d…m2B5tjYk

33f15848f9a67b…e2814b54c50dfe

6 in → 1 out2188.9900 XPM934 B

AcDhjHA9…ebukETHz

f10d8146327cfe…75b2c39a5a4d72

64 in → 2 out251.5851 XPM9.32 KB

AWnKomhJ…FLxy3cMe AaFBYBCA…frZ7727r

eb8c52a089b7ad…d25d1999401132

49 in → 2 out398.0460 XPM7.16 KB

AXrAqBjY…ELmUDY4U AdvLfhqF…YUuRFQZL

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.

2.917 × 10⁹⁵(96-digit number)

29172688047630588021…00612586099510353919

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

2.917 × 10⁹⁵(96-digit number)

29172688047630588021…00612586099510353919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.917 × 10⁹⁵(96-digit number)

29172688047630588021…00612586099510353921

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

5.834 × 10⁹⁵(96-digit number)

58345376095261176042…01225172199020707839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.834 × 10⁹⁵(96-digit number)

58345376095261176042…01225172199020707841

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

1.166 × 10⁹⁶(97-digit number)

11669075219052235208…02450344398041415679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.166 × 10⁹⁶(97-digit number)

11669075219052235208…02450344398041415681

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

2.333 × 10⁹⁶(97-digit number)

23338150438104470417…04900688796082831359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.333 × 10⁹⁶(97-digit number)

23338150438104470417…04900688796082831361

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

4.667 × 10⁹⁶(97-digit number)

46676300876208940834…09801377592165662719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.667 × 10⁹⁶(97-digit number)

46676300876208940834…09801377592165662721

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

Block #1,628,812

Cookie Preferences