Block #1,789,895

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/2/2016, 10:57:25 PM · Difficulty 10.7714 · 5,034,671 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77bd0fb62b195cb52bc24fe8e457431186d7cc1c960180bf0aba2e02d5de28e0

View on Chainz ↗

Height

#1,789,895

Difficulty

10.771405

Transactions

Size

5.90 KB

Version

Bits

0ac57ac7

Nonce

355,032,540

Timestamp

10/2/2016, 10:57:25 PM

Confirmations

5,034,671

Mined by

⛏️ P2SHATdSVaA4juvdVutf2SNvwEGtkrjHzP3obi

Merkle Root

06c770babc1bfe5bf27b8e43f922102313eb38380c963f85e126fe6d516db343

Transactions (2)

Coinbase16f3825e719b0a…ab49345b03a88a

1 in → 1 out8.6700 XPM109 B

ATdSVaA4…jHzP3obi

80c5c0cdd04ca1…0a10aede353b3d

39 in → 2 out311.1145 XPM5.71 KB

AdvLfhqF…YUuRFQZL AV16dvGJ…kgS7TVj2

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.

1.055 × 10⁹⁶(97-digit number)

10558666817324613654…86824368825253374079

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

1.055 × 10⁹⁶(97-digit number)

10558666817324613654…86824368825253374079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.055 × 10⁹⁶(97-digit number)

10558666817324613654…86824368825253374081

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

2.111 × 10⁹⁶(97-digit number)

21117333634649227309…73648737650506748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.111 × 10⁹⁶(97-digit number)

21117333634649227309…73648737650506748161

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

4.223 × 10⁹⁶(97-digit number)

42234667269298454618…47297475301013496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.223 × 10⁹⁶(97-digit number)

42234667269298454618…47297475301013496321

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

8.446 × 10⁹⁶(97-digit number)

84469334538596909236…94594950602026992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.446 × 10⁹⁶(97-digit number)

84469334538596909236…94594950602026992641

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

1.689 × 10⁹⁷(98-digit number)

16893866907719381847…89189901204053985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.689 × 10⁹⁷(98-digit number)

16893866907719381847…89189901204053985281

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 #1,789,895

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