Block #364,662

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 5:38:35 AM · Difficulty 10.4214 · 6,444,491 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

51a96f6de388185ea75c668d927794e46b7b7689d5fa2f0c7ab5820f7fa74813

View on Chainz ↗

Height

#364,662

Difficulty

10.421367

Transactions

Size

549 B

Version

Bits

0a6bdebd

Nonce

16,778,808

Timestamp

1/18/2014, 5:38:35 AM

Confirmations

6,444,491

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8f137a1f9251d7ff6120546bb7ec27946edc84b67295bcbaae1cae9cbbae54da

Transactions (2)

Coinbaseeb8bc15d3ab324…e5aa72e45deb9a

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

ad3b78ff34d48c…fc9491e41d0b04

2 in → 1 out5.9998 XPM339 B

ATMYSSTw…dhjN1tjK

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.

2.902 × 10¹⁰⁵(106-digit number)

29029156976093064904…11299629781781013439

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

2.902 × 10¹⁰⁵(106-digit number)

29029156976093064904…11299629781781013439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.902 × 10¹⁰⁵(106-digit number)

29029156976093064904…11299629781781013441

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

5.805 × 10¹⁰⁵(106-digit number)

58058313952186129809…22599259563562026879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.805 × 10¹⁰⁵(106-digit number)

58058313952186129809…22599259563562026881

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

1.161 × 10¹⁰⁶(107-digit number)

11611662790437225961…45198519127124053759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.161 × 10¹⁰⁶(107-digit number)

11611662790437225961…45198519127124053761

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

2.322 × 10¹⁰⁶(107-digit number)

23223325580874451923…90397038254248107519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.322 × 10¹⁰⁶(107-digit number)

23223325580874451923…90397038254248107521

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

4.644 × 10¹⁰⁶(107-digit number)

46446651161748903847…80794076508496215039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.644 × 10¹⁰⁶(107-digit number)

46446651161748903847…80794076508496215041

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 #364,662

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