Block #439,070

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 10:42:47 AM · Difficulty 10.3588 · 6,370,993 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6368a8613cd035777d886a8600c4516ebf25063429addbd2a76937e1f8ad6862

View on Chainz ↗

Height

#439,070

Difficulty

10.358838

Transactions

Size

936 B

Version

Bits

0a5bdcd0

Nonce

6,511

Timestamp

3/11/2014, 10:42:47 AM

Confirmations

6,370,993

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5ad217c5c5b25aba71557b441a5adb9e2986b2ee2262039e491edf0f5204e3a0

Transactions (1)

Coinbase5ad217c5c5b25a…1edf0f5204e3a0

1 in → 23 out9.3000 XPM845 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

2.046 × 10⁹⁶(97-digit number)

20460226985796099244…85887272833804426239

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

2.046 × 10⁹⁶(97-digit number)

20460226985796099244…85887272833804426239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.046 × 10⁹⁶(97-digit number)

20460226985796099244…85887272833804426241

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

4.092 × 10⁹⁶(97-digit number)

40920453971592198488…71774545667608852479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.092 × 10⁹⁶(97-digit number)

40920453971592198488…71774545667608852481

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

8.184 × 10⁹⁶(97-digit number)

81840907943184396977…43549091335217704959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.184 × 10⁹⁶(97-digit number)

81840907943184396977…43549091335217704961

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

1.636 × 10⁹⁷(98-digit number)

16368181588636879395…87098182670435409919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.636 × 10⁹⁷(98-digit number)

16368181588636879395…87098182670435409921

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

3.273 × 10⁹⁷(98-digit number)

32736363177273758791…74196365340870819839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.273 × 10⁹⁷(98-digit number)

32736363177273758791…74196365340870819841

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 #439,070

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