Block #236,798

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 4:44:18 PM · Difficulty 9.9485 · 6,568,144 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c01b0edfe363cd360927e12a3b8c05ec411859c2caf9fd9852003391714d942f

View on Chainz ↗

Height

#236,798

Difficulty

9.948476

Transactions

Size

2.36 KB

Version

Bits

09f2cf57

Nonce

201,027

Timestamp

10/31/2013, 4:44:18 PM

Confirmations

6,568,144

Mined by

⛏️ RrAYL7wcSt5Mgzig6YR6rjvXP4EfYuBetbPr

Merkle Root

b9c7ecd3d8234e4717b90742a4d135a9dd37a337c143920bec57033896cddfe8

Transactions (2)

Coinbaseeeeea66733753d…e67cea6c7968bf

1 in → 47 out10.0700 XPM1.62 KB

AYL7wcSt…YuBetbPr AeLaP1NX…SJ53Q2G7 ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

dbf6d83ca3f17c…2c4a0e3a31cbd3

4 in → 2 out2000.0100 XPM667 B

AKxjtQDX…UJJb3b6M Ab8SLw9T…QPgeqM7y

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.

1.060 × 10⁹²(93-digit number)

10609494817154149072…78800885964784539959

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

1.060 × 10⁹²(93-digit number)

10609494817154149072…78800885964784539959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.060 × 10⁹²(93-digit number)

10609494817154149072…78800885964784539961

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

2.121 × 10⁹²(93-digit number)

21218989634308298144…57601771929569079919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.121 × 10⁹²(93-digit number)

21218989634308298144…57601771929569079921

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

4.243 × 10⁹²(93-digit number)

42437979268616596289…15203543859138159839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.243 × 10⁹²(93-digit number)

42437979268616596289…15203543859138159841

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

8.487 × 10⁹²(93-digit number)

84875958537233192579…30407087718276319679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.487 × 10⁹²(93-digit number)

84875958537233192579…30407087718276319681

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

1.697 × 10⁹³(94-digit number)

16975191707446638515…60814175436552639359

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