Block #386,821

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 5:19:41 PM · Difficulty 10.4119 · 6,421,317 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2bcc39b65d46197b0eb007a42d5630d4cd68b8d34580e5e5186bcb3cac969463

View on Chainz ↗

Height

#386,821

Difficulty

10.411886

Transactions

Size

848 B

Version

Bits

0a69715a

Nonce

138,480

Timestamp

2/2/2014, 5:19:41 PM

Confirmations

6,421,317

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c28b7904643acdd922d0b0ccb08300572af25f58fb61f0e0da5ac529838638f4

Transactions (3)

Coinbasef63472bb8a5194…37c73767b30cb8

1 in → 1 out9.2371 XPM110 B

AeKNrjNj…1NEq95Ta

dca325d84a4617…ba82ebd9cf6785

1 in → 1 out9.1800 XPM157 B

AaLBYWdH…e9nxsSZs

8f45d3219f9909…76a0e5b08fc78b

3 in → 1 out9.0800 XPM488 B

AVCm4Pcc…q9XTCZ1S

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.

1.303 × 10¹⁰²(103-digit number)

13036195916522347340…11226468480291778559

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

1.303 × 10¹⁰²(103-digit number)

13036195916522347340…11226468480291778559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.303 × 10¹⁰²(103-digit number)

13036195916522347340…11226468480291778561

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

2.607 × 10¹⁰²(103-digit number)

26072391833044694680…22452936960583557119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.607 × 10¹⁰²(103-digit number)

26072391833044694680…22452936960583557121

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

5.214 × 10¹⁰²(103-digit number)

52144783666089389361…44905873921167114239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.214 × 10¹⁰²(103-digit number)

52144783666089389361…44905873921167114241

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

1.042 × 10¹⁰³(104-digit number)

10428956733217877872…89811747842334228479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.042 × 10¹⁰³(104-digit number)

10428956733217877872…89811747842334228481

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

2.085 × 10¹⁰³(104-digit number)

20857913466435755744…79623495684668456959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.085 × 10¹⁰³(104-digit number)

20857913466435755744…79623495684668456961

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 #386,821

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