Block #340,117

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 1:57:57 PM · Difficulty 10.1279 · 6,468,001 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2ad653dac3a12ec88cd5bb705044bae9e689f4b6f1d146ab4012a19dc2a5b6a

View on Chainz ↗

Height

#340,117

Difficulty

10.127887

Transactions

Size

2.20 KB

Version

Bits

0a20bd34

Nonce

334,949

Timestamp

1/2/2014, 1:57:57 PM

Confirmations

6,468,001

Mined by

⛏️ 0aRqAdnmwr7ciD5k8zTsT6cb3WR4aCBticWu6P

Merkle Root

b3e8fd70cb25857d2d861422fe2d85c465075c2a9ac9cbafe6f13850b46f9993

Transactions (4)

Coinbase3f097b87364aac…200647e853a6db

1 in → 22 out9.7300 XPM811 B

Adnmwr7c…BticWu6P AQ8QAT3J…rCFKuVbR AJzWx2VD…j4ZSMit5 AXeQnyEs…fUWKQwq8 APeshfYV…3PKcKMKH

cced91f5604dca…17cad8175640e4

6 in → 1 out9.4708 XPM930 B

AGqV9UoF…V2gwf5yv

cfceaa3cfea7de…1908dcc3283ced

1 in → 1 out0.9900 XPM193 B

AXuyzNP1…rXdTR4JB

61ef12a0eb23fb…344c7a3cb9c8c4

1 in → 2 out6.6387 XPM227 B

AVuQAwfn…UYbYYVWC AWNtHyfQ…hXa5dUTH

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.

1.586 × 10¹⁰¹(102-digit number)

15867224457128377697…70380415732517990399

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

1.586 × 10¹⁰¹(102-digit number)

15867224457128377697…70380415732517990399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.586 × 10¹⁰¹(102-digit number)

15867224457128377697…70380415732517990401

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

3.173 × 10¹⁰¹(102-digit number)

31734448914256755394…40760831465035980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.173 × 10¹⁰¹(102-digit number)

31734448914256755394…40760831465035980801

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

6.346 × 10¹⁰¹(102-digit number)

63468897828513510789…81521662930071961599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.346 × 10¹⁰¹(102-digit number)

63468897828513510789…81521662930071961601

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

1.269 × 10¹⁰²(103-digit number)

12693779565702702157…63043325860143923199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.269 × 10¹⁰²(103-digit number)

12693779565702702157…63043325860143923201

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

2.538 × 10¹⁰²(103-digit number)

25387559131405404315…26086651720287846399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.538 × 10¹⁰²(103-digit number)

25387559131405404315…26086651720287846401

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 #340,117

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