Block #390,758

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/5/2014, 9:05:39 AM · Difficulty 10.4259 · 6,411,909 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c3821cfd577a7ce86b13ad563d62d76aa854bd799df0869f3c0a5923d1b1d38

View on Chainz ↗

Height

#390,758

Difficulty

10.425933

Transactions

Size

1.23 KB

Version

Bits

0a6d09f2

Nonce

454,917

Timestamp

2/5/2014, 9:05:39 AM

Confirmations

6,411,909

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a35c4aaadf6ac1d522877c20e8f460ecc2b42f1a4e3072712a1f0ddd2fa2ea94

Transactions (2)

Coinbasee0e6eee21c0a66…f4cbbeee7b23c8

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

e9042d96d2b362…041a37b1a36cd2

5 in → 13 out39.5099 XPM1.03 KB

ASX9vJ7L…WFguM8AH Af5JcoF1…bCtmmgeZ AeKNrjNj…1NEq95Ta AXG8Wqsd…crHr1vLp AHx6AsKJ…1ijLBcnE

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.

3.271 × 10⁹³(94-digit number)

32711039530058830413…24718267902283521919

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

3.271 × 10⁹³(94-digit number)

32711039530058830413…24718267902283521919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.271 × 10⁹³(94-digit number)

32711039530058830413…24718267902283521921

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

6.542 × 10⁹³(94-digit number)

65422079060117660827…49436535804567043839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.542 × 10⁹³(94-digit number)

65422079060117660827…49436535804567043841

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

1.308 × 10⁹⁴(95-digit number)

13084415812023532165…98873071609134087679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.308 × 10⁹⁴(95-digit number)

13084415812023532165…98873071609134087681

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

2.616 × 10⁹⁴(95-digit number)

26168831624047064330…97746143218268175359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.616 × 10⁹⁴(95-digit number)

26168831624047064330…97746143218268175361

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

5.233 × 10⁹⁴(95-digit number)

52337663248094128661…95492286436536350719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.233 × 10⁹⁴(95-digit number)

52337663248094128661…95492286436536350721

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