Block #219,850

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 5:27:36 PM · Difficulty 9.9343 · 6,589,302 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

15ac97ade0a99cbfd6e38e02173a2c02d684375c646cdacfa9ffb63bacf485c8

View on Chainz ↗

Height

#219,850

Difficulty

9.934335

Transactions

Size

1.31 KB

Version

Bits

09ef308f

Nonce

61,783

Timestamp

10/20/2013, 5:27:36 PM

Confirmations

6,589,302

Mined by

⛏️ ZRdzAWZb1hL4JtNJXmB8RiXjR1EX4p63wEkMsn

Merkle Root

ee7a6b9218a4dedfcf093ab38b8a0272c63e296f2319258b21a456c94c5a438f

Transactions (1)

Coinbaseee7a6b9218a4de…a456c94c5a438f

1 in → 35 out10.1000 XPM1.22 KB

AWZb1hL4…63wEkMsn AbeUZSvK…ijGzuyjz Ab3dSvM7…Qoxxb9tp ARpndEmc…Hg792kEk AXpmXsTH…1zkdde3r

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.

5.116 × 10⁹⁶(97-digit number)

51165382995324142766…76126899445702232959

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

5.116 × 10⁹⁶(97-digit number)

51165382995324142766…76126899445702232959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.116 × 10⁹⁶(97-digit number)

51165382995324142766…76126899445702232961

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

1.023 × 10⁹⁷(98-digit number)

10233076599064828553…52253798891404465919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.023 × 10⁹⁷(98-digit number)

10233076599064828553…52253798891404465921

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

2.046 × 10⁹⁷(98-digit number)

20466153198129657106…04507597782808931839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.046 × 10⁹⁷(98-digit number)

20466153198129657106…04507597782808931841

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

4.093 × 10⁹⁷(98-digit number)

40932306396259314213…09015195565617863679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.093 × 10⁹⁷(98-digit number)

40932306396259314213…09015195565617863681

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

8.186 × 10⁹⁷(98-digit number)

81864612792518628426…18030391131235727359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.186 × 10⁹⁷(98-digit number)

81864612792518628426…18030391131235727361

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

Block #219,850

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