Block #360,008

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 4:33:54 AM · Difficulty 10.3879 · 6,454,804 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f4fddcceb03be4b0e13dffc5a5a7c76847fd377293df85ea7656ab345cd1e1d

View on Chainz ↗

Height

#360,008

Difficulty

10.387874

Transactions

Size

971 B

Version

Bits

0a634bb4

Nonce

8,367

Timestamp

1/15/2014, 4:33:54 AM

Confirmations

6,454,804

Mined by

⛏️ H~aRoiAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7e27bf3f3ee92c0fc836dbfc1a95558ae277ed792d778cbf929807cb4d9344c1

Transactions (1)

Coinbase7e27bf3f3ee92c…9807cb4d9344c1

1 in → 24 out9.2500 XPM879 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Ac5JXwCr…tf5C9dQa Aac9Hjdg…P4ktypc3 Ac7TsAMG…2W5MRTA8

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.

2.939 × 10⁹⁹(100-digit number)

29394512999130200369…22802936813048613439

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

2.939 × 10⁹⁹(100-digit number)

29394512999130200369…22802936813048613439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.939 × 10⁹⁹(100-digit number)

29394512999130200369…22802936813048613441

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

5.878 × 10⁹⁹(100-digit number)

58789025998260400738…45605873626097226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.878 × 10⁹⁹(100-digit number)

58789025998260400738…45605873626097226881

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

1.175 × 10¹⁰⁰(101-digit number)

11757805199652080147…91211747252194453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.175 × 10¹⁰⁰(101-digit number)

11757805199652080147…91211747252194453761

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

2.351 × 10¹⁰⁰(101-digit number)

23515610399304160295…82423494504388907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.351 × 10¹⁰⁰(101-digit number)

23515610399304160295…82423494504388907521

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

4.703 × 10¹⁰⁰(101-digit number)

47031220798608320591…64846989008777815039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.703 × 10¹⁰⁰(101-digit number)

47031220798608320591…64846989008777815041

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 #360,008

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