Block #357,188

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 6:11:38 AM · Difficulty 10.3824 · 6,455,452 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a2095c4b59b6fa2a69c4ea53a8d2f834d4bdc906fcfacea99e5dbdab772f6014

View on Chainz ↗

Height

#357,188

Difficulty

10.382419

Transactions

Size

1.05 KB

Version

Bits

0a61e63d

Nonce

26,570

Timestamp

1/13/2014, 6:11:38 AM

Confirmations

6,455,452

Mined by

⛏️ DsaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

96c77d7c6e7fefaba38d4693534662a72684ca63e66a6dd5235f1ac0e6c93fa3

Transactions (1)

Coinbase96c77d7c6e7fef…5f1ac0e6c93fa3

1 in → 27 out9.2600 XPM981 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AQwRN8bE…V8PsTcY9 AKzkYQaQ…zR4FspJZ

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.

1.207 × 10¹⁰¹(102-digit number)

12073785174897314729…27299044056526476799

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

1.207 × 10¹⁰¹(102-digit number)

12073785174897314729…27299044056526476799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.207 × 10¹⁰¹(102-digit number)

12073785174897314729…27299044056526476801

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

2.414 × 10¹⁰¹(102-digit number)

24147570349794629458…54598088113052953599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.414 × 10¹⁰¹(102-digit number)

24147570349794629458…54598088113052953601

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

4.829 × 10¹⁰¹(102-digit number)

48295140699589258917…09196176226105907199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.829 × 10¹⁰¹(102-digit number)

48295140699589258917…09196176226105907201

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

9.659 × 10¹⁰¹(102-digit number)

96590281399178517835…18392352452211814399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.659 × 10¹⁰¹(102-digit number)

96590281399178517835…18392352452211814401

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

1.931 × 10¹⁰²(103-digit number)

19318056279835703567…36784704904423628799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.931 × 10¹⁰²(103-digit number)

19318056279835703567…36784704904423628801

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

Block #357,188

Cookie Preferences