Block #13,866

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 2:44:45 PM · Difficulty 7.8089 · 6,780,379 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cb34d0ef785a476c23830930f34900581c2de156e5973e32bbea29c06926e36

View on Chainz ↗

Height

#13,866

Difficulty

7.808886

Transactions

Size

1.16 KB

Version

Bits

07cf1321

Nonce

893

Timestamp

7/11/2013, 2:44:45 PM

Confirmations

6,780,379

Merkle Root

d5d464ddb0f8e10cb5b0843173d0e90d8b89b9e1bb3279293e93e9ef159c21f9

Transactions (3)

Coinbase9bdb45cad87ae3…ac332445d37d0e

1 in → 1 out16.4000 XPM108 B

AH56WihZ…BTDE6ipk

8a894eedeb1beb…90e7daba4d6cf1

6 in → 2 out113.6500 XPM767 B

ASuR7ve9…mdUJdU3W ASoXp2As…edjAmBXG

9028a0cdb6c150…8adcd58e331189

1 in → 2 out17.7100 XPM226 B

AY3PeEX2…eTKB3ZF6 ATa3awxY…C1cwhm6J

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.

7.474 × 10⁹⁵(96-digit number)

74740740412502961688…79569706903199786789

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

7.474 × 10⁹⁵(96-digit number)

74740740412502961688…79569706903199786789

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.474 × 10⁹⁵(96-digit number)

74740740412502961688…79569706903199786791

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

1.494 × 10⁹⁶(97-digit number)

14948148082500592337…59139413806399573579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.494 × 10⁹⁶(97-digit number)

14948148082500592337…59139413806399573581

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

2.989 × 10⁹⁶(97-digit number)

29896296165001184675…18278827612799147159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.989 × 10⁹⁶(97-digit number)

29896296165001184675…18278827612799147161

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

5.979 × 10⁹⁶(97-digit number)

59792592330002369350…36557655225598294319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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