Block #794,511

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/2/2014, 11:06:18 PM · Difficulty 10.9750 · 6,013,977 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

191e2c16e9a83aa97c08a1542de004b3bc8935259548b4206de5942ecfc6b1d0

View on Chainz ↗

Height

#794,511

Difficulty

10.974964

Transactions

Size

3.17 KB

Version

Bits

0af9973e

Nonce

1,415,195,792

Timestamp

11/2/2014, 11:06:18 PM

Confirmations

6,013,977

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0836f2c9c89b9bbfa83add1b9c8ede3710921c55beead992ac25527eca1b7916

Transactions (2)

Coinbase6fd061c9ad9e96…fb2533bccc1cbd

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

a706ed00226640…035c36ef7c0907

20 in → 2 out20.0452 XPM2.97 KB

AUUZoAZw…2vtNGRG3 AJyoEnco…HToRvG4a

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.

4.580 × 10⁹⁵(96-digit number)

45801806804056969572…27065755130888998399

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

4.580 × 10⁹⁵(96-digit number)

45801806804056969572…27065755130888998399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.580 × 10⁹⁵(96-digit number)

45801806804056969572…27065755130888998401

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

9.160 × 10⁹⁵(96-digit number)

91603613608113939144…54131510261777996799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.160 × 10⁹⁵(96-digit number)

91603613608113939144…54131510261777996801

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

1.832 × 10⁹⁶(97-digit number)

18320722721622787828…08263020523555993599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.832 × 10⁹⁶(97-digit number)

18320722721622787828…08263020523555993601

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

3.664 × 10⁹⁶(97-digit number)

36641445443245575657…16526041047111987199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.664 × 10⁹⁶(97-digit number)

36641445443245575657…16526041047111987201

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

7.328 × 10⁹⁶(97-digit number)

73282890886491151315…33052082094223974399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.328 × 10⁹⁶(97-digit number)

73282890886491151315…33052082094223974401

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 #794,511

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