Block #344,112

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/5/2014, 2:35:20 AM · Difficulty 10.1894 · 6,457,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b510200b6caef22b7257a14ee8c7a36e9a7e21aab7f3eea9a6bbd52a69f99a14

View on Chainz ↗

Height

#344,112

Difficulty

10.189427

Transactions

Size

5.93 KB

Version

Bits

0a307e47

Nonce

4,122

Timestamp

1/5/2014, 2:35:20 AM

Confirmations

6,457,417

Mined by

⛏️ P2SHAXi1u8Tu5KiicP3TqyycEVpuJPKxq6Jwc4

Merkle Root

b151f8fab2aa4428028617674c6b7edbef85dfcce99381e151f2543dc5e0eff7

Transactions (5)

Coinbasec513714521ef29…6305a2ecbba245

1 in → 1 out9.7018 XPM109 B

AXi1u8Tu…Kxq6Jwc4

05e18f7cd63f4b…521f19ca8d2b69

7 in → 14 out40.2141 XPM1.35 KB

Ade3qZzB…o1FBN3Zf ANd83hMi…LyJo9381 AUp7TH4v…bf7ABCge AJnuijiE…CxRBB9HV AcKeq82d…Ym6LNchU

d618b2c9e872ca…8b42c69d6a7aef

22 in → 1 out6.3000 XPM3.22 KB

AGBXiVcn…NRKq7Pbv

997b5348450302…719224d5ad7de9

1 in → 2 out3.9216 XPM225 B

AMWhfZow…EH5vsb34 AdWKyAPx…nScwUY9N

18fa9063a0d3f6…a6dcb7bd705bda

6 in → 2 out1.0397 XPM967 B

AafgP6DA…yFh2eb88 AGusNSbi…TMhj3ShN

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.

3.579 × 10⁹⁹(100-digit number)

35796625545767671191…09927282448984951679

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

3.579 × 10⁹⁹(100-digit number)

35796625545767671191…09927282448984951679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.579 × 10⁹⁹(100-digit number)

35796625545767671191…09927282448984951681

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

7.159 × 10⁹⁹(100-digit number)

71593251091535342383…19854564897969903359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.159 × 10⁹⁹(100-digit number)

71593251091535342383…19854564897969903361

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

1.431 × 10¹⁰⁰(101-digit number)

14318650218307068476…39709129795939806719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.431 × 10¹⁰⁰(101-digit number)

14318650218307068476…39709129795939806721

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

2.863 × 10¹⁰⁰(101-digit number)

28637300436614136953…79418259591879613439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.863 × 10¹⁰⁰(101-digit number)

28637300436614136953…79418259591879613441

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

5.727 × 10¹⁰⁰(101-digit number)

57274600873228273907…58836519183759226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.727 × 10¹⁰⁰(101-digit number)

57274600873228273907…58836519183759226881

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