Block #186,571

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 11:37:45 PM · Difficulty 9.8669 · 6,618,791 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fd55779fa77f7ea87fe560ca04945adbbf510bb8c383a6a825d6a7622ab8a01

View on Chainz ↗

Height

#186,571

Difficulty

9.866855

Transactions

Size

1.44 KB

Version

Bits

09ddea39

Nonce

1,164,765,700

Timestamp

9/29/2013, 11:37:45 PM

Confirmations

6,618,791

Mined by

⛏️ RHIAJCCNvEZ7QwzTUEfYPwXoS9dvEgX1b1gmx

Merkle Root

d991e9071ba78f5e73a82362f1863f62295ce28372e2e75373f988341358c642

Transactions (1)

Coinbased991e9071ba78f…f988341358c642

1 in → 39 out10.2500 XPM1.36 KB

AJCCNvEZ…gX1b1gmx AP7ZfMBN…n8aVFt5X AJErs5Nt…zQVnq9U2 AV4rziFj…QhTLsLyZ AL7194fk…YNQBVjTB

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.

6.376 × 10⁹⁴(95-digit number)

63763086393709328958…29707758241299628799

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

6.376 × 10⁹⁴(95-digit number)

63763086393709328958…29707758241299628799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.376 × 10⁹⁴(95-digit number)

63763086393709328958…29707758241299628801

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

1.275 × 10⁹⁵(96-digit number)

12752617278741865791…59415516482599257599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.275 × 10⁹⁵(96-digit number)

12752617278741865791…59415516482599257601

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

2.550 × 10⁹⁵(96-digit number)

25505234557483731583…18831032965198515199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.550 × 10⁹⁵(96-digit number)

25505234557483731583…18831032965198515201

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

5.101 × 10⁹⁵(96-digit number)

51010469114967463166…37662065930397030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.101 × 10⁹⁵(96-digit number)

51010469114967463166…37662065930397030401

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

1.020 × 10⁹⁶(97-digit number)

10202093822993492633…75324131860794060799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.020 × 10⁹⁶(97-digit number)

10202093822993492633…75324131860794060801

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