Block #202,716

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 9:54:03 AM · Difficulty 9.8955 · 6,589,453 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9575e3c3bd8d31f12e0474d3954fff2bc39c0dd392aa99e9630ef35e115655f

View on Chainz ↗

Height

#202,716

Difficulty

9.895489

Transactions

Size

1.14 KB

Version

Bits

09e53ec9

Nonce

10,746

Timestamp

10/10/2013, 9:54:03 AM

Confirmations

6,589,453

Merkle Root

e430e274b3a155c18263b30adcc6032de232b26094377821fbcb04975ca2a501

Transactions (3)

Coinbase429bf1c4cb6fce…25b5e3cbea74e2

1 in → 1 out10.2300 XPM100 B

AaXb6Ldz…XefG91jF

3d2b6aff3066a1…592d086921ef9a

4 in → 2 out1442.5745 XPM669 B

AH8GcWsX…1ABJhdDL AN1MC7zL…PvKizWe3

59e71d8dce8649…384af08daa9adb

2 in → 1 out10.4200 XPM306 B

ARugjzc6…Vm1PtFHz

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.

3.017 × 10⁹⁵(96-digit number)

30172272383624178368…66824009597465194239

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

3.017 × 10⁹⁵(96-digit number)

30172272383624178368…66824009597465194239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.017 × 10⁹⁵(96-digit number)

30172272383624178368…66824009597465194241

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

6.034 × 10⁹⁵(96-digit number)

60344544767248356736…33648019194930388479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.034 × 10⁹⁵(96-digit number)

60344544767248356736…33648019194930388481

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

1.206 × 10⁹⁶(97-digit number)

12068908953449671347…67296038389860776959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.206 × 10⁹⁶(97-digit number)

12068908953449671347…67296038389860776961

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

2.413 × 10⁹⁶(97-digit number)

24137817906899342694…34592076779721553919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.413 × 10⁹⁶(97-digit number)

24137817906899342694…34592076779721553921

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

4.827 × 10⁹⁶(97-digit number)

48275635813798685389…69184153559443107839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.827 × 10⁹⁶(97-digit number)

48275635813798685389…69184153559443107841

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