Block #3,494,669

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/31/2019, 2:28:43 AM · Difficulty 10.9483 · 3,347,428 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8bff317f93d56760e8684009eea6eb93b3648cb0b47abae31a2b0cc6019a4757

View on Chainz ↗

Height

#3,494,669

Difficulty

10.948294

Transactions

Size

1.14 KB

Version

Bits

0af2c368

Nonce

1,643,558,140

Timestamp

12/31/2019, 2:28:43 AM

Confirmations

3,347,428

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

aa4e64038445c2eef6571b8c520c2ebd474a4183e94a7d07e9a965639946a1ba

Transactions (2)

Coinbase33222cdec3cd69…a22cc728426a9c

1 in → 1 out8.3500 XPM110 B

ASiq2qtK…VMhmk7yL

112ddeb33e72cb…53fe1b573eddd2

6 in → 2 out100.6180 XPM966 B

AaBHTdCx…5EynKCk3 AdmutZun…DoAzbe2Y

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.

1.503 × 10⁹⁴(95-digit number)

15038879225188585694…28317431928643951119

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

1.503 × 10⁹⁴(95-digit number)

15038879225188585694…28317431928643951119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.503 × 10⁹⁴(95-digit number)

15038879225188585694…28317431928643951121

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

3.007 × 10⁹⁴(95-digit number)

30077758450377171389…56634863857287902239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.007 × 10⁹⁴(95-digit number)

30077758450377171389…56634863857287902241

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

6.015 × 10⁹⁴(95-digit number)

60155516900754342778…13269727714575804479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.015 × 10⁹⁴(95-digit number)

60155516900754342778…13269727714575804481

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

1.203 × 10⁹⁵(96-digit number)

12031103380150868555…26539455429151608959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.203 × 10⁹⁵(96-digit number)

12031103380150868555…26539455429151608961

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

2.406 × 10⁹⁵(96-digit number)

24062206760301737111…53078910858303217919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.406 × 10⁹⁵(96-digit number)

24062206760301737111…53078910858303217921

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

4.812 × 10⁹⁵(96-digit number)

48124413520603474222…06157821716606435839

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 #3,494,669

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