Block #3,504,865

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2020, 5:28:32 AM · Difficulty 10.9306 · 3,328,931 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fa60c374455c9ec84733f58e08f10a0099c1eedc04b5eaa40366ab814af177e2

View on Chainz ↗

Height

#3,504,865

Difficulty

10.930596

Transactions

Size

7.45 KB

Version

Bits

0aee3b8d

Nonce

1,314,408,068

Timestamp

1/8/2020, 5:28:32 AM

Confirmations

3,328,931

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMz Visit pool ↗

Merkle Root

583405600618e2affaa6eb7a0650399c7ea04f0e966cd748a830b6aed8dc341f

Transactions (2)

Coinbase8e446795ee8557…563992daf69c10

1 in → 1 out8.4400 XPM109 B

AXfJqzUb…HXeXmjMz

69efa102b43284…ce8b30e59ed919

50 in → 1 out199.9200 XPM7.26 KB

ALcTQaSP…1C5Yf2Zi

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.

2.905 × 10⁹⁷(98-digit number)

29057793483064623472…61287047566394035199

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

2.905 × 10⁹⁷(98-digit number)

29057793483064623472…61287047566394035199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.905 × 10⁹⁷(98-digit number)

29057793483064623472…61287047566394035201

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

5.811 × 10⁹⁷(98-digit number)

58115586966129246945…22574095132788070399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.811 × 10⁹⁷(98-digit number)

58115586966129246945…22574095132788070401

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

1.162 × 10⁹⁸(99-digit number)

11623117393225849389…45148190265576140799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.162 × 10⁹⁸(99-digit number)

11623117393225849389…45148190265576140801

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

2.324 × 10⁹⁸(99-digit number)

23246234786451698778…90296380531152281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.324 × 10⁹⁸(99-digit number)

23246234786451698778…90296380531152281601

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

4.649 × 10⁹⁸(99-digit number)

46492469572903397556…80592761062304563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.649 × 10⁹⁸(99-digit number)

46492469572903397556…80592761062304563201

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 #3,504,865

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