Block #346,142

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 9:27:49 AM · Difficulty 10.2181 · 6,449,546 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9eaa2b710e1082a2e277158d948caf3afec0c5a53e999b621c248e512a6462f0

View on Chainz ↗

Height

#346,142

Difficulty

10.218122

Transactions

Size

7.32 KB

Version

Bits

0a37d6d0

Nonce

10,695

Timestamp

1/6/2014, 9:27:49 AM

Confirmations

6,449,546

Mined by

⛏️ P2SHAdNniXugpxxqC2NuYKf5nvRG1U7fNEKmZv

Merkle Root

f79fe5a8da72689894d13bc9136bbc5ef9c38fa88e4ef2f79a4dd1b4581ff5b6

Transactions (4)

Coinbase75d7ab8bff066e…f78cf699f72d76

1 in → 1 out9.6599 XPM109 B

AdNniXug…7fNEKmZv

282a76f8e0a7e8…de686431909a14

22 in → 2 out43.0753 XPM3.26 KB

Ae7KmoiF…xmgvwvbN ASPMWKVp…SbuT1BVu

4e89a5c4d1311f…e0e15acd4d364c

1 in → 7 out9.7100 XPM363 B

APPZLZRh…k8wT1gVi AQ9xKNXb…63CbHcWm AU9KdB9r…o5XC6WMy Aa3ZquZk…997XG4Ko AVchbZqV…dNDSTV4J

a0eef08d33e231…bc88c298bd93d0

24 in → 1 out71.6000 XPM3.51 KB

AXpHj8VG…p14M3hZe

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.

9.993 × 10⁹⁸(99-digit number)

99933211437139533588…04681083420360816239

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

9.993 × 10⁹⁸(99-digit number)

99933211437139533588…04681083420360816239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.993 × 10⁹⁸(99-digit number)

99933211437139533588…04681083420360816241

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

1.998 × 10⁹⁹(100-digit number)

19986642287427906717…09362166840721632479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.998 × 10⁹⁹(100-digit number)

19986642287427906717…09362166840721632481

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

3.997 × 10⁹⁹(100-digit number)

39973284574855813435…18724333681443264959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.997 × 10⁹⁹(100-digit number)

39973284574855813435…18724333681443264961

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

7.994 × 10⁹⁹(100-digit number)

79946569149711626871…37448667362886529919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.994 × 10⁹⁹(100-digit number)

79946569149711626871…37448667362886529921

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

1.598 × 10¹⁰⁰(101-digit number)

15989313829942325374…74897334725773059839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.598 × 10¹⁰⁰(101-digit number)

15989313829942325374…74897334725773059841

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