Block #322,887

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 7:44:45 AM · Difficulty 10.1942 · 6,493,335 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70d33deba91fa4ee348ae89f60562dfb0ef5021e246821609032284108d925e6

View on Chainz ↗

Height

#322,887

Difficulty

10.194192

Transactions

Size

1.71 KB

Version

Bits

0a31b698

Nonce

947,136

Timestamp

12/21/2013, 7:44:45 AM

Confirmations

6,493,335

Mined by

⛏️ GaRFkAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

e86e4f54be4496943d058c6f625842b05fff5c9ba5f9648c52939ff271c1f912

Transactions (4)

Coinbase6dedcd00c25c8b…d409c5a714c983

1 in → 27 out9.6100 XPM981 B

Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 AQ8QAT3J…rCFKuVbR ASWX42VM…XypQABkY AXmS7tZu…11YypHLP

02ffb46065d11b…86504ce3fa35fb

1 in → 2 out3.5024 XPM226 B

AaGHQTzh…Ampg1SzK AUra8Fjs…JccEirWj

15824700574678…a33ce9b1578022

1 in → 2 out3.1167 XPM226 B

AUxRLyVs…M5sWTALd APmxZSQy…D2TD6EjQ

697337d0e21a73…27c53237e4b334

1 in → 2 out1.9898 XPM226 B

AQzdW4BR…Bto5KcCL AU88giiE…4a2491qH

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.

1.887 × 10¹⁰¹(102-digit number)

18876950370461183488…81237830147258239679

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

1.887 × 10¹⁰¹(102-digit number)

18876950370461183488…81237830147258239679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.887 × 10¹⁰¹(102-digit number)

18876950370461183488…81237830147258239681

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

3.775 × 10¹⁰¹(102-digit number)

37753900740922366976…62475660294516479359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.775 × 10¹⁰¹(102-digit number)

37753900740922366976…62475660294516479361

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

7.550 × 10¹⁰¹(102-digit number)

75507801481844733953…24951320589032958719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.550 × 10¹⁰¹(102-digit number)

75507801481844733953…24951320589032958721

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

1.510 × 10¹⁰²(103-digit number)

15101560296368946790…49902641178065917439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.510 × 10¹⁰²(103-digit number)

15101560296368946790…49902641178065917441

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

3.020 × 10¹⁰²(103-digit number)

30203120592737893581…99805282356131834879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.020 × 10¹⁰²(103-digit number)

30203120592737893581…99805282356131834881

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 #322,887

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