Block #1,684,939

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/22/2016, 4:46:24 PM · Difficulty 10.7230 · 5,146,167 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

524b171f5f1761a2546164732c3a02be112575bf11dbdf5fbe82973e0b47b1b7

View on Chainz ↗

Height

#1,684,939

Difficulty

10.723010

Transactions

Size

427 B

Version

Bits

0ab91730

Nonce

78,150,031

Timestamp

7/22/2016, 4:46:24 PM

Confirmations

5,146,167

Mined by

⛏️ P2SHAbZEgXcVicT6Mhkku62UggWrXuPTGLVPUw

Merkle Root

02ac9e885f062d8ddd3f8a1c018b495611722733dcca538f171a11716615fa67

Transactions (2)

Coinbase25f847ae6dcf87…785b8a772c00ba

1 in → 1 out8.6900 XPM110 B

AbZEgXcV…PTGLVPUw

29f475f2b56394…b1510dcb414d84

1 in → 2 out0.2844 XPM227 B

AJKAupkn…faCte19y AUFj5yWY…T6TWkAR1

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.

2.142 × 10⁹⁵(96-digit number)

21422397758991216626…85125932783987589119

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

2.142 × 10⁹⁵(96-digit number)

21422397758991216626…85125932783987589119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.142 × 10⁹⁵(96-digit number)

21422397758991216626…85125932783987589121

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

4.284 × 10⁹⁵(96-digit number)

42844795517982433253…70251865567975178239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.284 × 10⁹⁵(96-digit number)

42844795517982433253…70251865567975178241

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

8.568 × 10⁹⁵(96-digit number)

85689591035964866507…40503731135950356479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.568 × 10⁹⁵(96-digit number)

85689591035964866507…40503731135950356481

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

1.713 × 10⁹⁶(97-digit number)

17137918207192973301…81007462271900712959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.713 × 10⁹⁶(97-digit number)

17137918207192973301…81007462271900712961

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

3.427 × 10⁹⁶(97-digit number)

34275836414385946602…62014924543801425919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.427 × 10⁹⁶(97-digit number)

34275836414385946602…62014924543801425921

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 #1,684,939

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