Block #341,688

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2014, 2:51:44 PM · Difficulty 10.1424 · 6,467,472 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f4b6d09f830b01dd7fc2cbf97439a1116bd2e8289735e7d654377a7dc8cc191

View on Chainz ↗

Height

#341,688

Difficulty

10.142352

Transactions

Size

1.05 KB

Version

Bits

0a247130

Nonce

17,125

Timestamp

1/3/2014, 2:51:44 PM

Confirmations

6,467,472

Mined by

⛏️ 6aRTAG5YAjechu8kNZ5eyyVJVz1YnBVhA4Aeh1

Merkle Root

a2b60a28f7221846de527bbc7f150d1f0a783dd92ae23f5dc330638c8c30ad4a

Transactions (1)

Coinbasea2b60a28f72218…30638c8c30ad4a

1 in → 27 out9.7100 XPM981 B

AG5YAjec…VhA4Aeh1 Ad9pSzHt…cpJ3y2zz AdwTEXyC…NwbVbqZV AamykSCW…5Mjzpr7i ASQBa4yz…5jpRWRVn

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.

3.629 × 10¹⁰⁰(101-digit number)

36290847722082777605…45822859831047791999

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

3.629 × 10¹⁰⁰(101-digit number)

36290847722082777605…45822859831047791999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.629 × 10¹⁰⁰(101-digit number)

36290847722082777605…45822859831047792001

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

7.258 × 10¹⁰⁰(101-digit number)

72581695444165555211…91645719662095583999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.258 × 10¹⁰⁰(101-digit number)

72581695444165555211…91645719662095584001

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

1.451 × 10¹⁰¹(102-digit number)

14516339088833111042…83291439324191167999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.451 × 10¹⁰¹(102-digit number)

14516339088833111042…83291439324191168001

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

2.903 × 10¹⁰¹(102-digit number)

29032678177666222084…66582878648382335999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.903 × 10¹⁰¹(102-digit number)

29032678177666222084…66582878648382336001

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

5.806 × 10¹⁰¹(102-digit number)

58065356355332444169…33165757296764671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.806 × 10¹⁰¹(102-digit number)

58065356355332444169…33165757296764672001

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 #341,688

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