Block #828,735

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/26/2014, 9:02:38 AM · Difficulty 10.9783 · 5,978,608 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ed0953ee421395c24070545cffc2f1cfa8d5e12efc5b0840d110e663a9772a7

View on Chainz ↗

Height

#828,735

Difficulty

10.978345

Transactions

Size

1.30 KB

Version

Bits

0afa74d4

Nonce

64,237,588

Timestamp

11/26/2014, 9:02:38 AM

Confirmations

5,978,608

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9a568f46a028cb64f0bc1187f8c7af1e605baa2eccdd00dcc6bac801b1581d87

Transactions (4)

Coinbase3edd86aaa28a0d…40cafcb4003156

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

0987c2daee8a6e…046a5666c5ce3a

4 in → 2 out30.8598 XPM669 B

AMvXHgvh…aGTnzs9H ALX1Sb5v…FWZWjFtY

e7525a19ef7a74…515a962fd75992

1 in → 2 out7.1326 XPM226 B

AdB7z2qg…oyGhBmdr AHRoBSh4…BSVTQ36Q

899ac82d0a015d…e4173ab9df8373

1 in → 2 out2.0564 XPM227 B

ALzV5Gwk…MZgg8VuT ALdwDaZj…NF9qw6Gb

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.

2.455 × 10⁹⁷(98-digit number)

24552193501217472970…52611015144577008319

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

2.455 × 10⁹⁷(98-digit number)

24552193501217472970…52611015144577008319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.455 × 10⁹⁷(98-digit number)

24552193501217472970…52611015144577008321

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

4.910 × 10⁹⁷(98-digit number)

49104387002434945940…05222030289154016639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.910 × 10⁹⁷(98-digit number)

49104387002434945940…05222030289154016641

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

9.820 × 10⁹⁷(98-digit number)

98208774004869891881…10444060578308033279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.820 × 10⁹⁷(98-digit number)

98208774004869891881…10444060578308033281

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

1.964 × 10⁹⁸(99-digit number)

19641754800973978376…20888121156616066559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.964 × 10⁹⁸(99-digit number)

19641754800973978376…20888121156616066561

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

3.928 × 10⁹⁸(99-digit number)

39283509601947956752…41776242313232133119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.928 × 10⁹⁸(99-digit number)

39283509601947956752…41776242313232133121

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

7.856 × 10⁹⁸(99-digit number)

78567019203895913504…83552484626464266239

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

Block #828,735

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