Block #235,854

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 4:29:03 AM · Difficulty 9.9462 · 6,568,157 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04d2dd4b4767a9973da70bd47561c3fb289483df26f907a40bcc6fbc7efae0dc

View on Chainz ↗

Height

#235,854

Difficulty

9.946189

Transactions

Size

3.24 KB

Version

Bits

09f23974

Nonce

95,857

Timestamp

10/31/2013, 4:29:03 AM

Confirmations

6,568,157

Mined by

⛏️ P2SHAYCiS6HuSLD1ekQ1SCgbXyR6xy37auXKDN

Merkle Root

605752887a89e691f7df9783bb5424c6c2888ccbd28da50e5e3b5d63e1e94191

Transactions (5)

Coinbase00f7cdd0fd881d…9cae9160fac44d

1 in → 1 out10.1500 XPM109 B

AYCiS6Hu…37auXKDN

1578e04b4c42d8…d83afe5962d88c

16 in → 2 out102.2731 XPM2.39 KB

AVGYH1h8…vsSDLsiG AYgE9mRb…bQgCvPxL

4f9330f4190061…ecddd837b939d4

1 in → 2 out10.0900 XPM227 B

ARuniCSJ…zxpwzHmX Abi3MacG…7v4ojCPB

d7442471cdb421…9a9069d9205514

1 in → 2 out8.0553 XPM227 B

ALz3uSwR…DHKjj4EL AHntHyUg…qqWKhrra

49b1c6907def52…bbfdc80fdeda60

1 in → 2 out4.7811 XPM226 B

AHQV2xhg…ahixs28K AFoCNcXV…jC6o6YsM

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.

1.092 × 10⁹⁵(96-digit number)

10922290187887174706…73416287473118023999

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

1.092 × 10⁹⁵(96-digit number)

10922290187887174706…73416287473118023999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.092 × 10⁹⁵(96-digit number)

10922290187887174706…73416287473118024001

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

2.184 × 10⁹⁵(96-digit number)

21844580375774349412…46832574946236047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.184 × 10⁹⁵(96-digit number)

21844580375774349412…46832574946236048001

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

4.368 × 10⁹⁵(96-digit number)

43689160751548698824…93665149892472095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.368 × 10⁹⁵(96-digit number)

43689160751548698824…93665149892472096001

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

8.737 × 10⁹⁵(96-digit number)

87378321503097397649…87330299784944191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.737 × 10⁹⁵(96-digit number)

87378321503097397649…87330299784944192001

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

1.747 × 10⁹⁶(97-digit number)

17475664300619479529…74660599569888383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.747 × 10⁹⁶(97-digit number)

17475664300619479529…74660599569888384001

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