Block #214,729

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 4:00:38 PM · Difficulty 9.9240 · 6,578,813 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ceefa5bc45e67d3018d83731a7488bff5ca2261393a70cc30c23b1828bb41d97

View on Chainz ↗

Height

#214,729

Difficulty

9.923995

Transactions

Size

4.53 KB

Version

Bits

09ec8aed

Nonce

1,164,754,566

Timestamp

10/17/2013, 4:00:38 PM

Confirmations

6,578,813

Merkle Root

4e87c27ac99cbaa0fbc47016c03512dc9aac3efd6dc2b3ce1c839d21d7fa71b0

Transactions (1)

Coinbase4e87c27ac99cba…839d21d7fa71b0

1 in → 132 out10.0867 XPM4.44 KB

AehSbrXS…x2Vu99iu AViH25QJ…kfkafa8f AWcD1GpL…2355pP1d ASb3steg…29Ya1XjB AH8yR9wQ…3GmoUBGQ

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.

4.330 × 10⁹⁶(97-digit number)

43309012006244947622…51617765386436550399

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

4.330 × 10⁹⁶(97-digit number)

43309012006244947622…51617765386436550399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.330 × 10⁹⁶(97-digit number)

43309012006244947622…51617765386436550401

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

8.661 × 10⁹⁶(97-digit number)

86618024012489895245…03235530772873100799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.661 × 10⁹⁶(97-digit number)

86618024012489895245…03235530772873100801

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

1.732 × 10⁹⁷(98-digit number)

17323604802497979049…06471061545746201599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.732 × 10⁹⁷(98-digit number)

17323604802497979049…06471061545746201601

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

3.464 × 10⁹⁷(98-digit number)

34647209604995958098…12942123091492403199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.464 × 10⁹⁷(98-digit number)

34647209604995958098…12942123091492403201

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

6.929 × 10⁹⁷(98-digit number)

69294419209991916196…25884246182984806399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.929 × 10⁹⁷(98-digit number)

69294419209991916196…25884246182984806401

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