Block #399,050

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 4:44:31 AM · Difficulty 10.4188 · 6,406,318 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cbcf51376daa231bc1816bf82c7d9e43b350cdb20f5358512685d34f5efe9aee

View on Chainz ↗

Height

#399,050

Difficulty

10.418850

Transactions

Size

1.50 KB

Version

Bits

0a6b39bb

Nonce

81,548

Timestamp

2/11/2014, 4:44:31 AM

Confirmations

6,406,318

Mined by

AN9emqpK7dgr5Ubo53Xd9AuJhzWEnrfX7s

Merkle Root

d537fe98d7081db585720b9340f3c4d6e513a91719406f61fa9088ef295118ae

Transactions (3)

Coinbase73c5fbab2212a5…cc20ed3f156aa6

1 in → 23 out9.2200 XPM845 B

AN9emqpK…WEnrfX7s Acs9SHrk…QJSB8SFG AczyTBWn…bEQQj33u AcgDwGo8…BBFwbjVo AKftjLGP…YtMg2x9D

fc5d3ea1d15539…97fda01f3c8cb6

1 in → 2 out7.1490 XPM226 B

AFreewNR…WwhUuhEf Aearh5b9…4jKZF3f9

a93220f814ea70…bf5502a1d95706

2 in → 2 out1.0141 XPM374 B

ANnkqFMR…96RVc4qV AUpNRwvv…jDcXjF82

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.

1.121 × 10⁹⁴(95-digit number)

11211281395559177678…88210906186174735359

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

1.121 × 10⁹⁴(95-digit number)

11211281395559177678…88210906186174735359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.121 × 10⁹⁴(95-digit number)

11211281395559177678…88210906186174735361

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

2.242 × 10⁹⁴(95-digit number)

22422562791118355357…76421812372349470719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.242 × 10⁹⁴(95-digit number)

22422562791118355357…76421812372349470721

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

4.484 × 10⁹⁴(95-digit number)

44845125582236710714…52843624744698941439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.484 × 10⁹⁴(95-digit number)

44845125582236710714…52843624744698941441

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

8.969 × 10⁹⁴(95-digit number)

89690251164473421428…05687249489397882879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.969 × 10⁹⁴(95-digit number)

89690251164473421428…05687249489397882881

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

1.793 × 10⁹⁵(96-digit number)

17938050232894684285…11374498978795765759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.793 × 10⁹⁵(96-digit number)

17938050232894684285…11374498978795765761

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