Block #386,355

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 10:04:38 AM · Difficulty 10.4080 · 6,405,855 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75eab8b6db6237d7220a9884cc1fc818e883754cdff03a7415fa7f01ff30be6e

View on Chainz ↗

Height

#386,355

Difficulty

10.407979

Transactions

Size

429 B

Version

Bits

0a687157

Nonce

2,498

Timestamp

2/2/2014, 10:04:38 AM

Confirmations

6,405,855

Merkle Root

a5d8b7b03ad1f42be4522b8b9abba79e76052c253870f771cb028c38981c1383

Transactions (2)

Coinbase1709b85d9a3bbe…b4a11134e1af55

1 in → 1 out9.2300 XPM109 B

ATssDQHU…PkY7ddv4

c7b6f1d0a0430c…1f21f25f4206ea

1 in → 2 out4.1252 XPM226 B

AVLTe17z…YZjG3pgV AJaRWYUg…Bc7zZ4Gg

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.

1.389 × 10¹⁰⁴(105-digit number)

13891146904310619344…14386361525425548799

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

1.389 × 10¹⁰⁴(105-digit number)

13891146904310619344…14386361525425548799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.389 × 10¹⁰⁴(105-digit number)

13891146904310619344…14386361525425548801

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

2.778 × 10¹⁰⁴(105-digit number)

27782293808621238689…28772723050851097599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.778 × 10¹⁰⁴(105-digit number)

27782293808621238689…28772723050851097601

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

5.556 × 10¹⁰⁴(105-digit number)

55564587617242477379…57545446101702195199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.556 × 10¹⁰⁴(105-digit number)

55564587617242477379…57545446101702195201

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

1.111 × 10¹⁰⁵(106-digit number)

11112917523448495475…15090892203404390399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.111 × 10¹⁰⁵(106-digit number)

11112917523448495475…15090892203404390401

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

2.222 × 10¹⁰⁵(106-digit number)

22225835046896990951…30181784406808780799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.222 × 10¹⁰⁵(106-digit number)

22225835046896990951…30181784406808780801

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