Block #369,429

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 9:58:40 AM · Difficulty 10.4440 · 6,456,015 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4725757a24288bd3977c74fa544d9e2e0be823677a8e8647192032d46fddc7bd

View on Chainz ↗

Height

#369,429

Difficulty

10.444046

Transactions

Size

461 B

Version

Bits

0a71acfc

Nonce

Timestamp

1/21/2014, 9:58:40 AM

Confirmations

6,456,015

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

a635b2bf50b6c472627f41f7f89715a088b1bb5765fd3c9ac3bfc652d026560e

Transactions (2)

Coinbase99ea616be298e3…23209697dbc18f

1 in → 2 out9.1600 XPM141 B

AdGRRh1e…QmctLb24 AHsw4d6U…EnM8UXNZ

141be54f902505…c79957ef64df87

1 in → 2 out3453.5386 XPM226 B

AVBe7e97…6VCFMgPQ AK9sHPxu…atsdX9MG

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.

3.039 × 10¹⁰³(104-digit number)

30390327594638761827…52371102790755311999

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

3.039 × 10¹⁰³(104-digit number)

30390327594638761827…52371102790755311999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.039 × 10¹⁰³(104-digit number)

30390327594638761827…52371102790755312001

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

6.078 × 10¹⁰³(104-digit number)

60780655189277523655…04742205581510623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.078 × 10¹⁰³(104-digit number)

60780655189277523655…04742205581510624001

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

1.215 × 10¹⁰⁴(105-digit number)

12156131037855504731…09484411163021247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.215 × 10¹⁰⁴(105-digit number)

12156131037855504731…09484411163021248001

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

2.431 × 10¹⁰⁴(105-digit number)

24312262075711009462…18968822326042495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.431 × 10¹⁰⁴(105-digit number)

24312262075711009462…18968822326042496001

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

4.862 × 10¹⁰⁴(105-digit number)

48624524151422018924…37937644652084991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.862 × 10¹⁰⁴(105-digit number)

48624524151422018924…37937644652084992001

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 #369,429

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