Block #1,799,777

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/9/2016, 6:36:55 PM · Difficulty 10.7746 · 5,014,263 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d61ef92cb244580d9b9c8bb09e28eebc7633f77bc882063f9de50308f1670424

View on Chainz ↗

Height

#1,799,777

Difficulty

10.774635

Transactions

Size

2.04 KB

Version

Bits

0ac64e81

Nonce

426,732,199

Timestamp

10/9/2016, 6:36:55 PM

Confirmations

5,014,263

Mined by

⛏️ P2SHATYNDKbXoJR6PGBNH5ay21kahJBLBCtDeH

Merkle Root

1413901909c9fddba2765173814ab806dfebef3ae0073e99729a2490e3f09429

Transactions (2)

Coinbaseeeccc96758d555…c40abfc68fd8da

1 in → 1 out8.6200 XPM110 B

ATYNDKbX…BLBCtDeH

12cf19e1e3d6a1…f4f71b6586ceec

1 in → 51 out16.5370 XPM1.85 KB

AbWFv1Kg…bddJVNnX AeKC8SAt…RuP19MAr AevhDukV…KuTgproh AHV6CKvh…aehtQR6F AdekwU1N…SwHf8fiB

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.

1.511 × 10⁹⁸(99-digit number)

15112944258240040001…17799909792535019519

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

1.511 × 10⁹⁸(99-digit number)

15112944258240040001…17799909792535019519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.511 × 10⁹⁸(99-digit number)

15112944258240040001…17799909792535019521

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

3.022 × 10⁹⁸(99-digit number)

30225888516480080002…35599819585070039039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.022 × 10⁹⁸(99-digit number)

30225888516480080002…35599819585070039041

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

6.045 × 10⁹⁸(99-digit number)

60451777032960160005…71199639170140078079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.045 × 10⁹⁸(99-digit number)

60451777032960160005…71199639170140078081

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

1.209 × 10⁹⁹(100-digit number)

12090355406592032001…42399278340280156159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.209 × 10⁹⁹(100-digit number)

12090355406592032001…42399278340280156161

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

2.418 × 10⁹⁹(100-digit number)

24180710813184064002…84798556680560312319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.418 × 10⁹⁹(100-digit number)

24180710813184064002…84798556680560312321

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 #1,799,777

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