Block #448,296

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 7:56:31 PM · Difficulty 10.3675 · 6,360,990 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2239fcb226e9778a9ec1c66de8909ade7c420b231aee41da81075848af028d3c

View on Chainz ↗

Height

#448,296

Difficulty

10.367501

Transactions

Size

4.04 KB

Version

Bits

0a5e148f

Nonce

642,228

Timestamp

3/17/2014, 7:56:31 PM

Confirmations

6,360,990

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

29c16ee57e28596c1e3755ba1cd827482da5dab52fc94b94bc306f40814f5a76

Transactions (3)

Coinbase70c78162da5760…96b337e8cb7b8e

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

7a47500170f671…123e1684166831

15 in → 1 out45.7823 XPM2.21 KB

ATsGimmm…XWTWknF1

f9f17ed0fc4593…c37decaa2a14a1

8 in → 22 out74.5800 XPM1.63 KB

AKMKG9Ws…WGGUSiN4 AUSw48r2…nRKXidTs ANLZBexf…uq7489uA Ae95cQjw…45QEqE1n AHbu8w6V…13P7BwSQ

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.

3.683 × 10⁹⁸(99-digit number)

36838853111594438185…15051723846840401919

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

3.683 × 10⁹⁸(99-digit number)

36838853111594438185…15051723846840401919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.683 × 10⁹⁸(99-digit number)

36838853111594438185…15051723846840401921

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

7.367 × 10⁹⁸(99-digit number)

73677706223188876370…30103447693680803839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.367 × 10⁹⁸(99-digit number)

73677706223188876370…30103447693680803841

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

1.473 × 10⁹⁹(100-digit number)

14735541244637775274…60206895387361607679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.473 × 10⁹⁹(100-digit number)

14735541244637775274…60206895387361607681

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

2.947 × 10⁹⁹(100-digit number)

29471082489275550548…20413790774723215359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.947 × 10⁹⁹(100-digit number)

29471082489275550548…20413790774723215361

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

5.894 × 10⁹⁹(100-digit number)

58942164978551101096…40827581549446430719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.894 × 10⁹⁹(100-digit number)

58942164978551101096…40827581549446430721

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 #448,296

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