Block #430,509

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 1:15:07 PM · Difficulty 10.3442 · 6,411,985 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3af78f72f2b69704ce903a5747486dd543a05823f889f93d6ef4b4a8ba368d8

View on Chainz ↗

Height

#430,509

Difficulty

10.344206

Transactions

Size

988 B

Version

Bits

0a581de0

Nonce

51,230

Timestamp

3/5/2014, 1:15:07 PM

Confirmations

6,411,985

Mined by

⛏️ P2SHAcgk5ySHVZYE842NUazS6uuQ6h9FXcEvUp

Merkle Root

e00922f0b59069d568b70ce0a2db10749411a6c6e29398279286cbfb9eded2f2

Transactions (2)

Coinbase6ee8669a243951…04adec84a02611

1 in → 1 out9.3400 XPM109 B

Acgk5ySH…9FXcEvUp

271cb4f92a2ef9…9f30cbcb922b71

5 in → 1 out1.5208 XPM786 B

ATj3X8Hn…UYDDsSJP

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.

2.268 × 10¹⁰¹(102-digit number)

22685737050138241197…14692577000851737919

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

2.268 × 10¹⁰¹(102-digit number)

22685737050138241197…14692577000851737919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.268 × 10¹⁰¹(102-digit number)

22685737050138241197…14692577000851737921

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

4.537 × 10¹⁰¹(102-digit number)

45371474100276482394…29385154001703475839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.537 × 10¹⁰¹(102-digit number)

45371474100276482394…29385154001703475841

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

9.074 × 10¹⁰¹(102-digit number)

90742948200552964789…58770308003406951679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.074 × 10¹⁰¹(102-digit number)

90742948200552964789…58770308003406951681

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

1.814 × 10¹⁰²(103-digit number)

18148589640110592957…17540616006813903359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.814 × 10¹⁰²(103-digit number)

18148589640110592957…17540616006813903361

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

3.629 × 10¹⁰²(103-digit number)

36297179280221185915…35081232013627806719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.629 × 10¹⁰²(103-digit number)

36297179280221185915…35081232013627806721

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 #430,509

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