Block #214,737

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 4:09:16 PM · Difficulty 9.9240 · 6,587,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ec8837482f1ff84c4e9252e12f9c0cf879b1877b3bf1dc714654e7dcb3d32fd

View on Chainz ↗

Height

#214,737

Difficulty

9.924049

Transactions

Size

722 B

Version

Bits

09ec8e78

Nonce

9,152

Timestamp

10/17/2013, 4:09:16 PM

Confirmations

6,587,760

Mined by

⛏️ P2SHALcsaFikPi7u5KkaRFGdxu4TvbmFEYkrKk

Merkle Root

bf4b204713db4bfab945912c032cb69eccfa3306e6c48b3e132706ca0843c3e5

Transactions (2)

Coinbasec91fa61b0a3345…d5dccd1fed9713

1 in → 1 out10.1500 XPM109 B

ALcsaFik…mFEYkrKk

ba5030b23d113c…0957be12bc5f44

3 in → 2 out2.7275 XPM522 B

AP4KumrA…TjGQoT6q AJM6aWAG…whFENXCA

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.

9.114 × 10⁹⁵(96-digit number)

91148480433232135977…07814476773871974079

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

9.114 × 10⁹⁵(96-digit number)

91148480433232135977…07814476773871974079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.114 × 10⁹⁵(96-digit number)

91148480433232135977…07814476773871974081

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

1.822 × 10⁹⁶(97-digit number)

18229696086646427195…15628953547743948159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.822 × 10⁹⁶(97-digit number)

18229696086646427195…15628953547743948161

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

3.645 × 10⁹⁶(97-digit number)

36459392173292854391…31257907095487896319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.645 × 10⁹⁶(97-digit number)

36459392173292854391…31257907095487896321

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

7.291 × 10⁹⁶(97-digit number)

72918784346585708782…62515814190975792639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.291 × 10⁹⁶(97-digit number)

72918784346585708782…62515814190975792641

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

1.458 × 10⁹⁷(98-digit number)

14583756869317141756…25031628381951585279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.458 × 10⁹⁷(98-digit number)

14583756869317141756…25031628381951585281

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