Block #3,429,400

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/12/2019, 1:16:19 AM · Difficulty 10.9805 · 3,397,441 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4da1d01f087bac592460dbe155967ccc1c8006c5d6d79ea44258be8948f8c1f1

View on Chainz ↗

Height

#3,429,400

Difficulty

10.980494

Transactions

Size

691 B

Version

Bits

0afb01a0

Nonce

511,795,900

Timestamp

11/12/2019, 1:16:19 AM

Confirmations

3,397,441

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

3140e01e8cabc65fa7d37cc0e0f43ed1c0aea218e42455c61b3b38dc5a13cc8b

Transactions (2)

Coinbasedee13ae78f1d41…7e0dcd0ce66278

1 in → 1 out8.2900 XPM110 B

ASiq2qtK…VMhmk7yL

1349f13a871398…dbdee267aa6f0b

3 in → 2 out11.0300 XPM490 B

AKTWSFwu…9Ub9eBb2 AMJq5v98…nvBEtQjJ

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.

1.859 × 10⁹⁸(99-digit number)

18593927737937205042…75446900350089789439

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

1.859 × 10⁹⁸(99-digit number)

18593927737937205042…75446900350089789439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.859 × 10⁹⁸(99-digit number)

18593927737937205042…75446900350089789441

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

3.718 × 10⁹⁸(99-digit number)

37187855475874410084…50893800700179578879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.718 × 10⁹⁸(99-digit number)

37187855475874410084…50893800700179578881

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

7.437 × 10⁹⁸(99-digit number)

74375710951748820169…01787601400359157759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.437 × 10⁹⁸(99-digit number)

74375710951748820169…01787601400359157761

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

1.487 × 10⁹⁹(100-digit number)

14875142190349764033…03575202800718315519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.487 × 10⁹⁹(100-digit number)

14875142190349764033…03575202800718315521

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

2.975 × 10⁹⁹(100-digit number)

29750284380699528067…07150405601436631039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.975 × 10⁹⁹(100-digit number)

29750284380699528067…07150405601436631041

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

5.950 × 10⁹⁹(100-digit number)

59500568761399056135…14300811202873262079

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 #3,429,400

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