Block #2,069,477

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/13/2017, 3:36:09 PM · Difficulty 10.8570 · 4,756,637 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

793598638243f79e2bfb6dd91ec956376e53fad489bef2ef32b2baab1998b088

View on Chainz ↗

Height

#2,069,477

Difficulty

10.857000

Transactions

Size

10.72 KB

Version

Bits

0adb6452

Nonce

1,226,903,644

Timestamp

4/13/2017, 3:36:09 PM

Confirmations

4,756,637

Mined by

⛏️ P2SHAZGqeETsD8vNehenTeRjReUD6iYrGQXtzW

Merkle Root

4f045dfceb5094a788781281c654e0d93dc15ec54f299a7999bd268d369ef215

Transactions (4)

Coinbase8a9250a8bf2fbf…4a7d21304fb79b

1 in → 1 out8.5900 XPM109 B

AZGqeETs…YrGQXtzW

70cae46bc824a7…4b00454f1b8548

1 in → 101 out199.9500 XPM3.51 KB

ANrJtTmh…88W1kbN4 AYa3zufz…4b7h4uio AdAwUfGC…Z2ei7fJf AZXABQei…gFtw78Jd AXdHjhXG…wnz77caG

414a5af5e2870d…d6e956df21fe0f

1 in → 101 out199.9500 XPM3.51 KB

AaUKv1jj…2iBxHv6m APymbE7o…yWrC9Wz1 AGZaRr1h…4Gj22dSv ANG3HyUY…LFKWzZCG AL8hLFRk…5p2eV5gV

2d29fa903f4cdd…90869170b30fb4

1 in → 101 out41.9642 XPM3.51 KB

APymbE7o…yWrC9Wz1 AZ3cZHxS…1qdoLqba AUuFSiRd…FK8uiVkw AJt8wXdi…TUyeU9DF ATtVt32D…EkfizmpZ

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.

2.645 × 10⁹⁵(96-digit number)

26454062449088590111…61540537573929886719

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

2.645 × 10⁹⁵(96-digit number)

26454062449088590111…61540537573929886719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.645 × 10⁹⁵(96-digit number)

26454062449088590111…61540537573929886721

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

5.290 × 10⁹⁵(96-digit number)

52908124898177180223…23081075147859773439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.290 × 10⁹⁵(96-digit number)

52908124898177180223…23081075147859773441

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

1.058 × 10⁹⁶(97-digit number)

10581624979635436044…46162150295719546879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.058 × 10⁹⁶(97-digit number)

10581624979635436044…46162150295719546881

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

2.116 × 10⁹⁶(97-digit number)

21163249959270872089…92324300591439093759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.116 × 10⁹⁶(97-digit number)

21163249959270872089…92324300591439093761

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

4.232 × 10⁹⁶(97-digit number)

42326499918541744178…84648601182878187519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.232 × 10⁹⁶(97-digit number)

42326499918541744178…84648601182878187521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.465 × 10⁹⁶(97-digit number)

84652999837083488357…69297202365756375039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,069,477

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