Block #1,634,850

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/19/2016, 12:39:21 AM · Difficulty 10.6164 · 5,182,866 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

784991c85895f1154c57783c7d677622060aa78f2d53e8ceb46c3a25c8a4765c

View on Chainz ↗

Height

#1,634,850

Difficulty

10.616422

Transactions

Size

2.01 KB

Version

Bits

0a9dcddc

Nonce

660,046,743

Timestamp

6/19/2016, 12:39:21 AM

Confirmations

5,182,866

Mined by

⛏️ P2SHAQsNVb1rDeepbN6auzLZ3nmtPkGuFjyudS

Merkle Root

873e123cb6b1a8d1f927c919c05d286f2d46eb7cf9f39f32dfc62400f5b5ff53

Transactions (2)

Coinbase2ae8c75139143c…9ccf4828a00aac

1 in → 1 out8.8800 XPM110 B

AQsNVb1r…GuFjyudS

0c5877cc26daa1…8527c7d9186dc9

12 in → 2 out417.5800 XPM1.82 KB

ALZ1fV2B…NDTZhmFF AcDhjHA9…ebukETHz

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.

7.092 × 10⁹⁶(97-digit number)

70924648221023273292…98543858232189378559

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

7.092 × 10⁹⁶(97-digit number)

70924648221023273292…98543858232189378559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.092 × 10⁹⁶(97-digit number)

70924648221023273292…98543858232189378561

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

1.418 × 10⁹⁷(98-digit number)

14184929644204654658…97087716464378757119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.418 × 10⁹⁷(98-digit number)

14184929644204654658…97087716464378757121

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

2.836 × 10⁹⁷(98-digit number)

28369859288409309317…94175432928757514239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.836 × 10⁹⁷(98-digit number)

28369859288409309317…94175432928757514241

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

5.673 × 10⁹⁷(98-digit number)

56739718576818618634…88350865857515028479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.673 × 10⁹⁷(98-digit number)

56739718576818618634…88350865857515028481

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

1.134 × 10⁹⁸(99-digit number)

11347943715363723726…76701731715030056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.134 × 10⁹⁸(99-digit number)

11347943715363723726…76701731715030056961

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 #1,634,850

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