Block #379,001

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 6:26:35 AM · Difficulty 10.4129 · 6,438,066 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7cd21bd7b8fc8077db0a3f93d2d31905aa8bd9fbf58c43088af9229bdd59b352

View on Chainz ↗

Height

#379,001

Difficulty

10.412916

Transactions

Size

1.23 KB

Version

Bits

0a69b4de

Nonce

8,518

Timestamp

1/28/2014, 6:26:35 AM

Confirmations

6,438,066

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

86e2097b6e62884141a76d37519f48d5554e3464671074492ebb4b689f775f14

Transactions (2)

Coinbase2d0826924cc390…a187737d3b1cc4

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

e1a05be00c2359…4169a942c52edb

5 in → 13 out37.6507 XPM1.03 KB

AP7TwgeU…YnzWXXj4 AX7i163C…WxTE9wuc APEZp5zy…DtHkNUxw ALHk9Q3e…tWb1Xjm9 AL7VQmgs…Eosw369P

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.

9.598 × 10⁹⁷(98-digit number)

95987463650677351065…99934257132820045199

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

9.598 × 10⁹⁷(98-digit number)

95987463650677351065…99934257132820045199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.598 × 10⁹⁷(98-digit number)

95987463650677351065…99934257132820045201

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

1.919 × 10⁹⁸(99-digit number)

19197492730135470213…99868514265640090399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.919 × 10⁹⁸(99-digit number)

19197492730135470213…99868514265640090401

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

3.839 × 10⁹⁸(99-digit number)

38394985460270940426…99737028531280180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.839 × 10⁹⁸(99-digit number)

38394985460270940426…99737028531280180801

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

7.678 × 10⁹⁸(99-digit number)

76789970920541880852…99474057062560361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.678 × 10⁹⁸(99-digit number)

76789970920541880852…99474057062560361601

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

1.535 × 10⁹⁹(100-digit number)

15357994184108376170…98948114125120723199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.535 × 10⁹⁹(100-digit number)

15357994184108376170…98948114125120723201

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 #379,001

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