Block #235,059

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/30/2013, 4:56:30 PM · Difficulty 9.9451 · 6,571,692 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4583ac6c7d179cbfe3d42a2606cb6a3166ea3158f44ef8858219cbddeaff6f7

View on Chainz ↗

Height

#235,059

Difficulty

9.945060

Transactions

Size

1.94 KB

Version

Bits

09f1ef73

Nonce

22,944

Timestamp

10/30/2013, 4:56:30 PM

Confirmations

6,571,692

Mined by

⛏️ 3Rq9KAc5sZcdPRNjfrTK9pchLQrJN4XkzV4eckG

Merkle Root

b315dfd6d9263cb6d293dbac1aad7752deb750003c6c5f96b0c7300f2d56e8bd

Transactions (1)

Coinbaseb315dfd6d9263c…c7300f2d56e8bd

1 in → 54 out10.0800 XPM1.85 KB

Ac5sZcdP…kzV4eckG ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ANUaggy4…MWdrertQ AQZYfdBZ…DVLcLRg8

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.

2.352 × 10⁹³(94-digit number)

23522851424111630953…79975593539816767099

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

2.352 × 10⁹³(94-digit number)

23522851424111630953…79975593539816767099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.352 × 10⁹³(94-digit number)

23522851424111630953…79975593539816767101

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

4.704 × 10⁹³(94-digit number)

47045702848223261907…59951187079633534199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.704 × 10⁹³(94-digit number)

47045702848223261907…59951187079633534201

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

9.409 × 10⁹³(94-digit number)

94091405696446523814…19902374159267068399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.409 × 10⁹³(94-digit number)

94091405696446523814…19902374159267068401

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

1.881 × 10⁹⁴(95-digit number)

18818281139289304762…39804748318534136799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.881 × 10⁹⁴(95-digit number)

18818281139289304762…39804748318534136801

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

3.763 × 10⁹⁴(95-digit number)

37636562278578609525…79609496637068273599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.763 × 10⁹⁴(95-digit number)

37636562278578609525…79609496637068273601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.527 × 10⁹⁴(95-digit number)

75273124557157219051…59218993274136547199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #235,059

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