Block #259,242

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 12:35:08 PM · Difficulty 9.9771 · 6,549,993 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6c2f69b12483b1c57ae9426fbd2448f98c970128b92c2ec4f62d90a18099c48

View on Chainz ↗

Height

#259,242

Difficulty

9.977117

Transactions

Size

1.97 KB

Version

Bits

09fa245e

Nonce

24,136

Timestamp

11/13/2013, 12:35:08 PM

Confirmations

6,549,993

Mined by

⛏️ P2SHAQ8aAtez3T6cM5xfd4XFdi5h1Sw2oepPBa

Merkle Root

4686a22a0bc93ef91caaf4893919f0bf26be9d4b5bb25f9e1c1cca2acecda634

Transactions (4)

Coinbasef7a13c86cade20…48f10dbb070bf7

1 in → 1 out10.0600 XPM109 B

AQ8aAtez…w2oepPBa

28ac21aca47320…20797c2ebd5588

3 in → 7 out20.4339 XPM624 B

AeKNrjNj…1NEq95Ta AZ3PWPr3…T7o8gD2E AUocmdjW…iZFk1bBs AcDNU6SH…pREhxuLA AL7194fk…YNQBVjTB

0470ab338015eb…3ea74ad4254943

1 in → 2 out107.6291 XPM226 B

ASCnHxth…3eXz7vXu AZdmkNt9…Dk8ffFeU

e3a628b3d75a24…7fa3bc2556fa31

6 in → 2 out19.7908 XPM967 B

AZdmkNt9…Dk8ffFeU AKQCj4F2…vxDNvRJh

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.

1.107 × 10⁹¹(92-digit number)

11071777159028690464…00451096887495916959

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

1.107 × 10⁹¹(92-digit number)

11071777159028690464…00451096887495916959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.107 × 10⁹¹(92-digit number)

11071777159028690464…00451096887495916961

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

2.214 × 10⁹¹(92-digit number)

22143554318057380929…00902193774991833919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.214 × 10⁹¹(92-digit number)

22143554318057380929…00902193774991833921

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

4.428 × 10⁹¹(92-digit number)

44287108636114761858…01804387549983667839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.428 × 10⁹¹(92-digit number)

44287108636114761858…01804387549983667841

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

8.857 × 10⁹¹(92-digit number)

88574217272229523717…03608775099967335679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.857 × 10⁹¹(92-digit number)

88574217272229523717…03608775099967335681

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

1.771 × 10⁹²(93-digit number)

17714843454445904743…07217550199934671359

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

Block #259,242

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