Block #236,381

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 11:26:31 AM · Difficulty 9.9473 · 6,574,222 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abc41c0d32959af1b856ef7d187797f09702bf43c3d2a12bdf111be001b54646

View on Chainz ↗

Height

#236,381

Difficulty

9.947309

Transactions

Size

1.68 KB

Version

Bits

09f282d2

Nonce

9,707

Timestamp

10/31/2013, 11:26:31 AM

Confirmations

6,574,222

Mined by

⛏️ Rr>r-AMypZdXSN9SRf28auDeE3guPFj5jJKu8wP

Merkle Root

72911bcf026d5c0fe16f54d4babc8f3a56e5bfc1e4b7ab8d80d49e12da6cb1b8

Transactions (1)

Coinbase72911bcf026d5c…d49e12da6cb1b8

1 in → 46 out10.0700 XPM1.59 KB

AMypZdXS…5jJKu8wP APVGazMT…cDCk2nwA AMVsYFfp…DB9jn4fb AJaGRnaj…iCHGoy6E AWZb1hL4…63wEkMsn

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.

2.972 × 10⁹⁷(98-digit number)

29728486185426569882…02451552917225226239

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

2.972 × 10⁹⁷(98-digit number)

29728486185426569882…02451552917225226239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.972 × 10⁹⁷(98-digit number)

29728486185426569882…02451552917225226241

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

5.945 × 10⁹⁷(98-digit number)

59456972370853139764…04903105834450452479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.945 × 10⁹⁷(98-digit number)

59456972370853139764…04903105834450452481

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

1.189 × 10⁹⁸(99-digit number)

11891394474170627952…09806211668900904959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.189 × 10⁹⁸(99-digit number)

11891394474170627952…09806211668900904961

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

2.378 × 10⁹⁸(99-digit number)

23782788948341255905…19612423337801809919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.378 × 10⁹⁸(99-digit number)

23782788948341255905…19612423337801809921

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

4.756 × 10⁹⁸(99-digit number)

47565577896682511811…39224846675603619839

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

Block #236,381

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