Block #250,371

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 11:27:36 AM · Difficulty 9.9682 · 6,580,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b93753316e3867bed74930c43392d6c4028efbd3dda5ea474c35ca5d35f0b04a

View on Chainz ↗

Height

#250,371

Difficulty

9.968207

Transactions

Size

6.96 KB

Version

Bits

09f7dc68

Nonce

13,233

Timestamp

11/8/2013, 11:27:36 AM

Confirmations

6,580,173

Mined by

⛏️ P2SHAM2vrwSSvJgXzt8ghnje8Wh3xGAfbCGwrh

Merkle Root

0c0646d7da7699b8ab982809f7f559e65b501645de198de5d18e858d0744714a

Transactions (3)

Coinbase7a1bf7935b0429…68cf80acd30c22

1 in → 1 out10.1400 XPM109 B

AM2vrwSS…AfbCGwrh

9fa46818500e3f…caf5baf7f5e550

45 in → 1 out6.0000 XPM6.55 KB

ASuAQ3GG…gzJge6LC

782475cd6ce03f…6bf08c9fb38685

1 in → 2 out3.9832 XPM226 B

ARskhKeb…UgDvvX9P ALtRahbV…gBHcM9RB

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.

9.944 × 10⁹⁹(100-digit number)

99445651604711679202…99457260930585796479

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

9.944 × 10⁹⁹(100-digit number)

99445651604711679202…99457260930585796479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.944 × 10⁹⁹(100-digit number)

99445651604711679202…99457260930585796481

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

1.988 × 10¹⁰⁰(101-digit number)

19889130320942335840…98914521861171592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.988 × 10¹⁰⁰(101-digit number)

19889130320942335840…98914521861171592961

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

3.977 × 10¹⁰⁰(101-digit number)

39778260641884671680…97829043722343185919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.977 × 10¹⁰⁰(101-digit number)

39778260641884671680…97829043722343185921

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

7.955 × 10¹⁰⁰(101-digit number)

79556521283769343361…95658087444686371839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.955 × 10¹⁰⁰(101-digit number)

79556521283769343361…95658087444686371841

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

1.591 × 10¹⁰¹(102-digit number)

15911304256753868672…91316174889372743679

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 #250,371

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