Block #418,859

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 5:10:22 AM · Difficulty 10.3831 · 6,395,184 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

344e1f9e582ab07ddca5cf4f6394ed83803097874174a763d2e1a98825381760

View on Chainz ↗

Height

#418,859

Difficulty

10.383110

Transactions

Size

1.54 KB

Version

Bits

0a62137c

Nonce

11,092

Timestamp

2/25/2014, 5:10:22 AM

Confirmations

6,395,184

Mined by

⛏️ +daS%xAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b63c4fa032d62e42cdb3a7ad41e5d86314bb3e39506801276141466dcf2e5cc8

Transactions (4)

Coinbase76ca262accbab0…97f2b8d249557d

1 in → 22 out9.2600 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

6cce3d4b3d4843…f0d474c066c3ba

1 in → 2 out8.1788 XPM226 B

AGAMt16a…4LVibYA3 APAjMExd…Yn6D2sLq

28ecb2203f95ec…fc7a1c3c6f09a6

1 in → 2 out3.1645 XPM225 B

AMWhfZow…EH5vsb34 AdBEYoLK…ZUAmrfSC

23562396bae50b…6ee7a879f808fe

1 in → 2 out7.1644 XPM226 B

AMUugv36…qJqLnmaJ AYpTPKQ7…cm6wV2fo

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.

2.887 × 10¹⁰⁰(101-digit number)

28879575739399668659…88428007804757453119

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

2.887 × 10¹⁰⁰(101-digit number)

28879575739399668659…88428007804757453119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.887 × 10¹⁰⁰(101-digit number)

28879575739399668659…88428007804757453121

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

5.775 × 10¹⁰⁰(101-digit number)

57759151478799337319…76856015609514906239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.775 × 10¹⁰⁰(101-digit number)

57759151478799337319…76856015609514906241

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

1.155 × 10¹⁰¹(102-digit number)

11551830295759867463…53712031219029812479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.155 × 10¹⁰¹(102-digit number)

11551830295759867463…53712031219029812481

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

2.310 × 10¹⁰¹(102-digit number)

23103660591519734927…07424062438059624959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.310 × 10¹⁰¹(102-digit number)

23103660591519734927…07424062438059624961

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

4.620 × 10¹⁰¹(102-digit number)

46207321183039469855…14848124876119249919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.620 × 10¹⁰¹(102-digit number)

46207321183039469855…14848124876119249921

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 #418,859

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