Block #218,802

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 3:38:22 AM · Difficulty 9.9314 · 6,589,165 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d61d81e4d65df461575b5be1065fa08a2ae5661baab150d5ba554a2d934fca3

View on Chainz ↗

Height

#218,802

Difficulty

9.931414

Transactions

Size

1.86 KB

Version

Bits

09ee7125

Nonce

1,028

Timestamp

10/20/2013, 3:38:22 AM

Confirmations

6,589,165

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

d785b5e7545a3ba75569a56d339a9a08770432545bb6e140fb319ee6a66a057e

Transactions (3)

Coinbaseca5353799cf775…f0e9e75b90eb4d

1 in → 1 out10.1500 XPM110 B

AbuU1HhS…JPwsJEbB

6e0f56d6f2f045…a9d999ae7fc3de

4 in → 8 out40.5500 XPM737 B

AGyvi7x2…vr95keMt ARR7aRH6…ne3DXGXZ AbuU1HhS…JPwsJEbB AT2w9AM1…YMN7C8VV AL7194fk…YNQBVjTB

c7a3a18ca9e458…df0cc78742bd10

6 in → 2 out2.0116 XPM967 B

Aak3JWif…NaNCKpE5 AYnYq3tx…HEEwDZRP

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.

2.703 × 10¹⁰²(103-digit number)

27035464879433882094…24774574730644951039

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

2.703 × 10¹⁰²(103-digit number)

27035464879433882094…24774574730644951039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.703 × 10¹⁰²(103-digit number)

27035464879433882094…24774574730644951041

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

5.407 × 10¹⁰²(103-digit number)

54070929758867764188…49549149461289902079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.407 × 10¹⁰²(103-digit number)

54070929758867764188…49549149461289902081

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

1.081 × 10¹⁰³(104-digit number)

10814185951773552837…99098298922579804159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.081 × 10¹⁰³(104-digit number)

10814185951773552837…99098298922579804161

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

2.162 × 10¹⁰³(104-digit number)

21628371903547105675…98196597845159608319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.162 × 10¹⁰³(104-digit number)

21628371903547105675…98196597845159608321

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

4.325 × 10¹⁰³(104-digit number)

43256743807094211350…96393195690319216639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.325 × 10¹⁰³(104-digit number)

43256743807094211350…96393195690319216641

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 #218,802

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