Block #60,695

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 9:25:42 AM · Difficulty 8.9702 · 6,735,690 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c06b45f2f69cdfdcfed804fd125c229749ab1d86fc7255ee36a8985c4fade296

View on Chainz ↗

Height

#60,695

Difficulty

8.970239

Transactions

Size

205 B

Version

Bits

08f86197

Nonce

356

Timestamp

7/18/2013, 9:25:42 AM

Confirmations

6,735,690

Mined by

⛏️ P2SHAXkJn6CMwgEQfjDS5VTGC9t8wjHxMPiiDY

Merkle Root

d91f886a1a2185f17bc8a8b212181b31054dd5697e56d00330f0ad6125d81712

Transactions (1)

Coinbased91f886a1a2185…f0ad6125d81712

1 in → 1 out12.4100 XPM110 B

AXkJn6CM…HxMPiiDY

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.

6.388 × 10¹⁰⁵(106-digit number)

63882780197398650784…06494129091523266299

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

6.388 × 10¹⁰⁵(106-digit number)

63882780197398650784…06494129091523266299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.388 × 10¹⁰⁵(106-digit number)

63882780197398650784…06494129091523266301

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

1.277 × 10¹⁰⁶(107-digit number)

12776556039479730156…12988258183046532599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.277 × 10¹⁰⁶(107-digit number)

12776556039479730156…12988258183046532601

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

2.555 × 10¹⁰⁶(107-digit number)

25553112078959460313…25976516366093065199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.555 × 10¹⁰⁶(107-digit number)

25553112078959460313…25976516366093065201

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

5.110 × 10¹⁰⁶(107-digit number)

51106224157918920627…51953032732186130399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.110 × 10¹⁰⁶(107-digit number)

51106224157918920627…51953032732186130401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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