Block #794,542

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/2/2014, 11:37:25 PM · Difficulty 10.9750 · 6,022,639 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e58a59650fd553a4e73f9bff3b646aae6cbc2cc5f75c86f7cefa8f398b979fba

View on Chainz ↗

Height

#794,542

Difficulty

10.974972

Transactions

Size

657 B

Version

Bits

0af997be

Nonce

404,952,244

Timestamp

11/2/2014, 11:37:25 PM

Confirmations

6,022,639

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a288bdaf6f891875d81bcaaf40123da2d1a3eb814226a20f85010dfb5b4954fb

Transactions (3)

Coinbase98eb579c05ecf9…b58e6081eceadf

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

6d17471dd2ef9b…9f86848b049c29

1 in → 2 out1.5107 XPM225 B

Ad9ygyTf…jNFpKfiv AcAAHAsy…fD4ceoxt

c1334ffaa4d9e8…2a1e33be2f537e

1 in → 2 out0.5192 XPM226 B

AWeFTqSF…usRDA3NM AV6ANdiV…HjDen4uU

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.

1.017 × 10⁹⁶(97-digit number)

10173925151685461093…98564669862847167359

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

1.017 × 10⁹⁶(97-digit number)

10173925151685461093…98564669862847167359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.017 × 10⁹⁶(97-digit number)

10173925151685461093…98564669862847167361

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

2.034 × 10⁹⁶(97-digit number)

20347850303370922187…97129339725694334719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.034 × 10⁹⁶(97-digit number)

20347850303370922187…97129339725694334721

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

4.069 × 10⁹⁶(97-digit number)

40695700606741844374…94258679451388669439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.069 × 10⁹⁶(97-digit number)

40695700606741844374…94258679451388669441

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

8.139 × 10⁹⁶(97-digit number)

81391401213483688749…88517358902777338879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.139 × 10⁹⁶(97-digit number)

81391401213483688749…88517358902777338881

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

1.627 × 10⁹⁷(98-digit number)

16278280242696737749…77034717805554677759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.627 × 10⁹⁷(98-digit number)

16278280242696737749…77034717805554677761

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

3.255 × 10⁹⁷(98-digit number)

32556560485393475499…54069435611109355519

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 #794,542

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