Block #369,579

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 12:07:55 PM · Difficulty 10.4464 · 6,447,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62478ed58fd12682c14c1e0e1ee743565bb8307f45069ae0afc0b8f96bdb4bfb

View on Chainz ↗

Height

#369,579

Difficulty

10.446380

Transactions

Size

1.69 KB

Version

Bits

0a7245fb

Nonce

200,812

Timestamp

1/21/2014, 12:07:55 PM

Confirmations

6,447,255

Mined by

⛏️ aRbAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

420fb705c944fa97d52efb3d3f1dbb97a07b604efe0bf1cb9d3d55c2c8f161c4

Transactions (4)

Coinbase7005d5e86e4783…27ef856da15866

1 in → 22 out9.1500 XPM811 B

AQvZBsUo…hppgRZTJ Ac5JXwCr…tf5C9dQa Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6

1e441ba68c52cf…243efe592590d0

1 in → 2 out7.1229 XPM227 B

AZW7nmo4…baQG5or7 ATQTPdot…Sgh9Kgnn

7b36c495066da0…cf44eea3448e0a

1 in → 2 out6.0995 XPM226 B

Ab7eGsNs…SfonyKLU AWhqCNs1…mTz9bU71

6bdfe82c87c087…297200d3b56da8

2 in → 2 out5.1616 XPM374 B

AaQBDPVV…AKpKWug2 APGwyDGe…hLT3eM37

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.

2.490 × 10⁸⁹(90-digit number)

24902080261482604275…40986006706170748639

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

2.490 × 10⁸⁹(90-digit number)

24902080261482604275…40986006706170748639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.490 × 10⁸⁹(90-digit number)

24902080261482604275…40986006706170748641

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

4.980 × 10⁸⁹(90-digit number)

49804160522965208551…81972013412341497279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.980 × 10⁸⁹(90-digit number)

49804160522965208551…81972013412341497281

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

9.960 × 10⁸⁹(90-digit number)

99608321045930417102…63944026824682994559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.960 × 10⁸⁹(90-digit number)

99608321045930417102…63944026824682994561

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

1.992 × 10⁹⁰(91-digit number)

19921664209186083420…27888053649365989119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.992 × 10⁹⁰(91-digit number)

19921664209186083420…27888053649365989121

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

3.984 × 10⁹⁰(91-digit number)

39843328418372166840…55776107298731978239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.984 × 10⁹⁰(91-digit number)

39843328418372166840…55776107298731978241

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 #369,579

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