Block #473,388

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 9:04:52 PM · Difficulty 10.4467 · 6,351,555 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3314a0d1f468cb0dbd1310d2f1f28b1f63230db90219e3befadd3f1c12bf8482

View on Chainz ↗

Height

#473,388

Difficulty

10.446673

Transactions

Size

880 B

Version

Bits

0a725926

Nonce

12,019,548

Timestamp

4/3/2014, 9:04:52 PM

Confirmations

6,351,555

Mined by

⛏️ P2SHATX97UayxEKc7u5MAvSRXVWwrKDjJ5SaUw

Merkle Root

959e6ee746554a6f750968c425a795d9036c7618b50eb9514ceb78c106df5c8a

Transactions (4)

Coinbaseb4884f197d3666…e2130c30bd2ad4

1 in → 1 out9.1800 XPM109 B

ATX97Uay…DjJ5SaUw

7c0cc8d071e173…fefd7d40a7a041

1 in → 2 out8.1385 XPM227 B

AKenikHZ…Ykids9rS ATwvNNEL…MGLhkX9C

5c4e232a81a11c…07c3b83b5b6871

1 in → 2 out6.6259 XPM226 B

AeB5HmMq…mCGHeD8p AQB9US1u…F5Ahmqux

3a338631230a12…b7174769858b7c

1 in → 2 out2.2130 XPM227 B

AL5oEDax…iTJ9YNEc APVnYHpK…1CK3YDkW

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.

6.222 × 10⁹⁵(96-digit number)

62229463294497177291…13929019230044981759

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

6.222 × 10⁹⁵(96-digit number)

62229463294497177291…13929019230044981759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.222 × 10⁹⁵(96-digit number)

62229463294497177291…13929019230044981761

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

1.244 × 10⁹⁶(97-digit number)

12445892658899435458…27858038460089963519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.244 × 10⁹⁶(97-digit number)

12445892658899435458…27858038460089963521

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

2.489 × 10⁹⁶(97-digit number)

24891785317798870916…55716076920179927039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.489 × 10⁹⁶(97-digit number)

24891785317798870916…55716076920179927041

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

4.978 × 10⁹⁶(97-digit number)

49783570635597741833…11432153840359854079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.978 × 10⁹⁶(97-digit number)

49783570635597741833…11432153840359854081

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

9.956 × 10⁹⁶(97-digit number)

99567141271195483666…22864307680719708159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.956 × 10⁹⁶(97-digit number)

99567141271195483666…22864307680719708161

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 #473,388

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