Block #293,913

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 2:12:46 PM · Difficulty 9.9908 · 6,515,258 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc5b225bbba5c9446ca6dcc8e8ea64c0e35d3685a83748fef687b2706e0be96c

View on Chainz ↗

Height

#293,913

Difficulty

9.990816

Transactions

Size

1.11 KB

Version

Bits

09fda61c

Nonce

171,855

Timestamp

12/4/2013, 2:12:46 PM

Confirmations

6,515,258

Mined by

⛏️ |aR82?AXtX1eVTeTSAVT6Zc3EjFqNPckmCZ7tu6S

Merkle Root

33f5b698b178bf0f25801b1f0e3590f2cd53894dddf8f32bc146127c4de5a030

Transactions (1)

Coinbase33f5b698b178bf…46127c4de5a030

1 in → 29 out9.9800 XPM1.02 KB

AXtX1eVT…mCZ7tu6S AY4LyZBe…7DTvswxY AasHKD21…wZrMJcVH Ad9pSzHt…cpJ3y2zz AS6sqK6K…qy9tzTmq

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.

3.605 × 10⁹³(94-digit number)

36059287967290876433…12742706678280129759

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

3.605 × 10⁹³(94-digit number)

36059287967290876433…12742706678280129759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.605 × 10⁹³(94-digit number)

36059287967290876433…12742706678280129761

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

7.211 × 10⁹³(94-digit number)

72118575934581752867…25485413356560259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.211 × 10⁹³(94-digit number)

72118575934581752867…25485413356560259521

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

1.442 × 10⁹⁴(95-digit number)

14423715186916350573…50970826713120519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.442 × 10⁹⁴(95-digit number)

14423715186916350573…50970826713120519041

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

2.884 × 10⁹⁴(95-digit number)

28847430373832701147…01941653426241038079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.884 × 10⁹⁴(95-digit number)

28847430373832701147…01941653426241038081

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

5.769 × 10⁹⁴(95-digit number)

57694860747665402294…03883306852482076159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.769 × 10⁹⁴(95-digit number)

57694860747665402294…03883306852482076161

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 #293,913

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