Block #215,048

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 8:22:27 PM · Difficulty 9.9249 · 6,576,504 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7d4c539374b0e2775087dab1f11f71bf3f8fad25b6ccd9e38fef90b9907d0c33

View on Chainz ↗

Height

#215,048

Difficulty

9.924852

Transactions

Size

390 B

Version

Bits

09ecc314

Nonce

47,353

Timestamp

10/17/2013, 8:22:27 PM

Confirmations

6,576,504

Merkle Root

71f5f340832aa75017dd33d1f5691f2b5040c24ea617c72eddb6e77dae78637a

Transactions (2)

Coinbaseac3eb3ae3b8530…4573d24dde9d4c

1 in → 1 out10.1500 XPM109 B

ATaEUvKp…Jgvuxagg

354f2d5110cf73…3f232ed0c21c4d

1 in → 2 out10.1500 XPM191 B

AHXtUaPq…GL391bZK AQAvQSWZ…C9mFkvux

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.

1.588 × 10⁹⁵(96-digit number)

15883668847714045645…89783193011424337919

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

1.588 × 10⁹⁵(96-digit number)

15883668847714045645…89783193011424337919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.588 × 10⁹⁵(96-digit number)

15883668847714045645…89783193011424337921

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

3.176 × 10⁹⁵(96-digit number)

31767337695428091291…79566386022848675839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.176 × 10⁹⁵(96-digit number)

31767337695428091291…79566386022848675841

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

6.353 × 10⁹⁵(96-digit number)

63534675390856182583…59132772045697351679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.353 × 10⁹⁵(96-digit number)

63534675390856182583…59132772045697351681

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

1.270 × 10⁹⁶(97-digit number)

12706935078171236516…18265544091394703359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.270 × 10⁹⁶(97-digit number)

12706935078171236516…18265544091394703361

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

2.541 × 10⁹⁶(97-digit number)

25413870156342473033…36531088182789406719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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