Block #804,256

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/9/2014, 5:18:48 PM · Difficulty 10.9754 · 5,993,895 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

840fb7f12a933f9cfc777c0a142b3114472e15bd6420b2667c77eace8ac68bf8

View on Chainz ↗

Height

#804,256

Difficulty

10.975352

Transactions

Size

1.08 KB

Version

Bits

0af9b0b3

Nonce

136,419,843

Timestamp

11/9/2014, 5:18:48 PM

Confirmations

5,993,895

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

475bae8ef3552e6c5acf5efcd9704505d7f783e7c5e5daea21b00a4440cde73b

Transactions (3)

Coinbase5f987df708329d…a985d017dade9d

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

16deab755ef383…6e74a202231fce

4 in → 2 out8.8277 XPM671 B

APgeEFGV…Mi9CLSBE AcNoqDVK…kUf6UExG

d61e4138ec0819…9b74b0b8141ca3

1 in → 2 out4.2900 XPM227 B

AbwD3oAB…6mThcBNv AbFJHDk8…PBzZicHZ

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.

5.919 × 10⁹⁸(99-digit number)

59197273455598596210…89588358606122420799

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

5.919 × 10⁹⁸(99-digit number)

59197273455598596210…89588358606122420799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.919 × 10⁹⁸(99-digit number)

59197273455598596210…89588358606122420801

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

1.183 × 10⁹⁹(100-digit number)

11839454691119719242…79176717212244841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.183 × 10⁹⁹(100-digit number)

11839454691119719242…79176717212244841601

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

2.367 × 10⁹⁹(100-digit number)

23678909382239438484…58353434424489683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.367 × 10⁹⁹(100-digit number)

23678909382239438484…58353434424489683201

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

4.735 × 10⁹⁹(100-digit number)

47357818764478876968…16706868848979366399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.735 × 10⁹⁹(100-digit number)

47357818764478876968…16706868848979366401

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

9.471 × 10⁹⁹(100-digit number)

94715637528957753936…33413737697958732799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.471 × 10⁹⁹(100-digit number)

94715637528957753936…33413737697958732801

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

1.894 × 10¹⁰⁰(101-digit number)

18943127505791550787…66827475395917465599

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