Block #372,229

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2014, 10:59:32 AM · Difficulty 10.4291 · 6,443,764 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cee02285e3d009e4eef070781562d60603eba75c5966ee22adf9e6fdc5f31b4

View on Chainz ↗

Height

#372,229

Difficulty

10.429146

Transactions

Size

428 B

Version

Bits

0a6ddc84

Nonce

646,764

Timestamp

1/23/2014, 10:59:32 AM

Confirmations

6,443,764

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5cd9724b8680a0bd1b02184fdf0c8a65217f779b8231979c562b2e04b597e9f7

Transactions (2)

Coinbase995efd3fd034dd…a583e61100df31

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

4ca5b302fabab8…59b2d0f08544be

1 in → 2 out3.9517 XPM226 B

Abm71H12…wpc6H13v ANKifPwS…SeSppJvY

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.

7.338 × 10⁹⁹(100-digit number)

73382696764902106602…52454058522636345919

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

7.338 × 10⁹⁹(100-digit number)

73382696764902106602…52454058522636345919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.338 × 10⁹⁹(100-digit number)

73382696764902106602…52454058522636345921

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

1.467 × 10¹⁰⁰(101-digit number)

14676539352980421320…04908117045272691839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.467 × 10¹⁰⁰(101-digit number)

14676539352980421320…04908117045272691841

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

2.935 × 10¹⁰⁰(101-digit number)

29353078705960842641…09816234090545383679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.935 × 10¹⁰⁰(101-digit number)

29353078705960842641…09816234090545383681

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

5.870 × 10¹⁰⁰(101-digit number)

58706157411921685282…19632468181090767359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.870 × 10¹⁰⁰(101-digit number)

58706157411921685282…19632468181090767361

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

1.174 × 10¹⁰¹(102-digit number)

11741231482384337056…39264936362181534719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.174 × 10¹⁰¹(102-digit number)

11741231482384337056…39264936362181534721

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 #372,229

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