Block #904,338

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2015, 8:01:19 PM · Difficulty 10.9374 · 5,903,162 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be833c237f45526cc79bc2876614751e5bb534c65b6ec07f8a85d3223338ec2d

View on Chainz ↗

Height

#904,338

Difficulty

10.937403

Transactions

Size

5.34 KB

Version

Bits

0aeff9a2

Nonce

69,517,294

Timestamp

1/21/2015, 8:01:19 PM

Confirmations

5,903,162

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

eed3ce87f527c7b786678f66015837a80b420efe348730c85d902da445106e54

Transactions (2)

Coinbase92b8e40f80025d…af027396ad6c89

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

4741f442a63115…25dfde28826647

35 in → 2 out5059.8900 XPM5.14 KB

AZMunvRb…G9pQh9ak ATi5Moaj…DouiPxQE

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.

1.271 × 10⁹⁸(99-digit number)

12711393000406850023…03290245583125381119

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

1.271 × 10⁹⁸(99-digit number)

12711393000406850023…03290245583125381119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.271 × 10⁹⁸(99-digit number)

12711393000406850023…03290245583125381121

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

2.542 × 10⁹⁸(99-digit number)

25422786000813700047…06580491166250762239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.542 × 10⁹⁸(99-digit number)

25422786000813700047…06580491166250762241

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

5.084 × 10⁹⁸(99-digit number)

50845572001627400095…13160982332501524479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.084 × 10⁹⁸(99-digit number)

50845572001627400095…13160982332501524481

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

1.016 × 10⁹⁹(100-digit number)

10169114400325480019…26321964665003048959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.016 × 10⁹⁹(100-digit number)

10169114400325480019…26321964665003048961

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

2.033 × 10⁹⁹(100-digit number)

20338228800650960038…52643929330006097919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.033 × 10⁹⁹(100-digit number)

20338228800650960038…52643929330006097921

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 #904,338

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