Block #469,223

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 1:59:10 AM · Difficulty 10.4288 · 6,320,856 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e96f133d89ffd30e2b2532af3d8c2b3889ea256fec8d6ef8636129e99729fd3

View on Chainz ↗

Height

#469,223

Difficulty

10.428850

Transactions

Size

682 B

Version

Bits

0a6dc91d

Nonce

868,609

Timestamp

4/1/2014, 1:59:10 AM

Confirmations

6,320,856

Merkle Root

042fe745ea15de85d72662bb17b8e1fb1f5d639167b51f1bf34f010b2bfe0ea0

Transactions (2)

Coinbase7b5ae5511baf38…4f4cb6a3ea674f

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

fe553fe70c61fd…51b7320b7c9421

2 in → 7 out18.3700 XPM478 B

AVbjNLpc…e1xsNhVz AQEx65ab…Sn8HJuB1 AeKNrjNj…1NEq95Ta AVrD6maY…W77cdqzz Aai7rmvE…JWhtS5Q5

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.

2.437 × 10¹⁰³(104-digit number)

24373688084965438445…66412121032166617599

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

2.437 × 10¹⁰³(104-digit number)

24373688084965438445…66412121032166617599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.437 × 10¹⁰³(104-digit number)

24373688084965438445…66412121032166617601

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

4.874 × 10¹⁰³(104-digit number)

48747376169930876890…32824242064333235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.874 × 10¹⁰³(104-digit number)

48747376169930876890…32824242064333235201

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

9.749 × 10¹⁰³(104-digit number)

97494752339861753780…65648484128666470399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.749 × 10¹⁰³(104-digit number)

97494752339861753780…65648484128666470401

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

1.949 × 10¹⁰⁴(105-digit number)

19498950467972350756…31296968257332940799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.949 × 10¹⁰⁴(105-digit number)

19498950467972350756…31296968257332940801

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

3.899 × 10¹⁰⁴(105-digit number)

38997900935944701512…62593936514665881599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.899 × 10¹⁰⁴(105-digit number)

38997900935944701512…62593936514665881601

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