Block #234,568

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 9:47:45 AM · Difficulty 9.9443 · 6,568,966 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ecb5e67d74c8f5401f7ee0a7f1143f87a3f3afaa502869e07eea33c012039c70

View on Chainz ↗

Height

#234,568

Difficulty

9.944286

Transactions

Size

1.94 KB

Version

Bits

09f1bcba

Nonce

3,909

Timestamp

10/30/2013, 9:47:45 AM

Confirmations

6,568,966

Mined by

⛏️ HRp#ATrmN1ij3g2zGMYWrzfvEbVTBvYtpqEH7e

Merkle Root

ba46e5bbe7c66f86c8e06dad7f1d77fb0a841964b6cf969a0b76dffabc829b63

Transactions (1)

Coinbaseba46e5bbe7c66f…76dffabc829b63

1 in → 54 out10.0800 XPM1.85 KB

ATrmN1ij…YtpqEH7e AFqKfjez…qX9Ace3g AabHNb1B…GRoingRy ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

5.289 × 10⁹³(94-digit number)

52897635114820330204…50194219223666477439

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

5.289 × 10⁹³(94-digit number)

52897635114820330204…50194219223666477439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.289 × 10⁹³(94-digit number)

52897635114820330204…50194219223666477441

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

1.057 × 10⁹⁴(95-digit number)

10579527022964066040…00388438447332954879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.057 × 10⁹⁴(95-digit number)

10579527022964066040…00388438447332954881

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

2.115 × 10⁹⁴(95-digit number)

21159054045928132081…00776876894665909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.115 × 10⁹⁴(95-digit number)

21159054045928132081…00776876894665909761

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

4.231 × 10⁹⁴(95-digit number)

42318108091856264163…01553753789331819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.231 × 10⁹⁴(95-digit number)

42318108091856264163…01553753789331819521

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

8.463 × 10⁹⁴(95-digit number)

84636216183712528326…03107507578663639039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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