Block #387,661

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/3/2014, 7:04:53 AM · Difficulty 10.4138 · 6,413,197 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee7201061b8fd53fe9d32053f9806ae861b4361e0d01d170b6627ff86e5802a6

View on Chainz ↗

Height

#387,661

Difficulty

10.413841

Transactions

Size

1.27 KB

Version

Bits

0a69f180

Nonce

15,736

Timestamp

2/3/2014, 7:04:53 AM

Confirmations

6,413,197

Mined by

⛏️ M&7Acs9SHrkBk52E7r7T3v7yemDoFQJSB8SFG

Merkle Root

c726dc0d9cc376b1f6554f26fce3ed8a295469feceaa89bc8da2c683ffccc016

Transactions (3)

Coinbase1cce0b08741f7b…05006044e29f4d

1 in → 18 out9.2332 XPM675 B

Acs9SHrk…QJSB8SFG AUzEPJFG…kYkA5U9V APJPNQaM…8nyTxzkW ATLD7BNP…nPjXCb2h AMunqLwt…nFnv4dvR

3849eb45c413f3…9f457ee39a232d

2 in → 1 out80.0900 XPM340 B

AKjZyZX7…1xqeruo9

a1d599c936eb6b…7d885e59651d3f

1 in → 1 out3.0000 XPM192 B

AdzdvG9Z…BeEabsDT

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.

6.179 × 10⁹⁹(100-digit number)

61797323986891992106…58452253178293137599

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

6.179 × 10⁹⁹(100-digit number)

61797323986891992106…58452253178293137599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.179 × 10⁹⁹(100-digit number)

61797323986891992106…58452253178293137601

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

1.235 × 10¹⁰⁰(101-digit number)

12359464797378398421…16904506356586275199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.235 × 10¹⁰⁰(101-digit number)

12359464797378398421…16904506356586275201

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

2.471 × 10¹⁰⁰(101-digit number)

24718929594756796842…33809012713172550399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.471 × 10¹⁰⁰(101-digit number)

24718929594756796842…33809012713172550401

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

4.943 × 10¹⁰⁰(101-digit number)

49437859189513593685…67618025426345100799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.943 × 10¹⁰⁰(101-digit number)

49437859189513593685…67618025426345100801

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

9.887 × 10¹⁰⁰(101-digit number)

98875718379027187371…35236050852690201599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.887 × 10¹⁰⁰(101-digit number)

98875718379027187371…35236050852690201601

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