Block #1,943,799

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2017, 9:53:53 PM · Difficulty 10.7719 · 4,872,219 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16a984d0fe2c73d241957d5403379544d3a34bc42a4e7045a23d21806f2c3776

View on Chainz ↗

Height

#1,943,799

Difficulty

10.771923

Transactions

Size

6.78 KB

Version

Bits

0ac59cc2

Nonce

496,296,957

Timestamp

1/17/2017, 9:53:53 PM

Confirmations

4,872,219

Mined by

⛏️ P2SHAd1vwDuGcvR7j7YYwCoY2UuQVfF7WhtwLX

Merkle Root

12a78d0ba4400f3d54a78b843a92376b0eba7e12a89608695c94d51ae9e38a85

Transactions (3)

Coinbasec5b137a1f85a4b…be4199a4f32547

1 in → 1 out8.6800 XPM109 B

Ad1vwDuG…F7WhtwLX

e45c2d30e8c348…2fabfc54437d4f

1 in → 95 out98.7272 XPM3.31 KB

ANiTFZMA…ufBYqC23 AKhwDZUm…g1NVdk5D APZ6uQRc…EW7u1vMJ AaUKv1jj…2iBxHv6m AToPf9AB…9h8ivZji

1bde244adb337e…0686b9cee8d3d6

1 in → 94 out26.7234 XPM3.28 KB

AQyQpPuC…1QVBtCcr AW71osBv…3HNu8eEh AeBGfHbW…BLvSjEAh APW3V7Ar…vbaXF9M6 ATbpcJdV…jpYz3kW4

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.

6.348 × 10⁹⁶(97-digit number)

63484379473385240942…67526824668201451519

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

6.348 × 10⁹⁶(97-digit number)

63484379473385240942…67526824668201451519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.348 × 10⁹⁶(97-digit number)

63484379473385240942…67526824668201451521

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

1.269 × 10⁹⁷(98-digit number)

12696875894677048188…35053649336402903039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.269 × 10⁹⁷(98-digit number)

12696875894677048188…35053649336402903041

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

2.539 × 10⁹⁷(98-digit number)

25393751789354096376…70107298672805806079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.539 × 10⁹⁷(98-digit number)

25393751789354096376…70107298672805806081

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

5.078 × 10⁹⁷(98-digit number)

50787503578708192753…40214597345611612159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.078 × 10⁹⁷(98-digit number)

50787503578708192753…40214597345611612161

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

1.015 × 10⁹⁸(99-digit number)

10157500715741638550…80429194691223224319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.015 × 10⁹⁸(99-digit number)

10157500715741638550…80429194691223224321

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 #1,943,799

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