Block #225,407

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/24/2013, 11:17:01 AM · Difficulty 9.9367 · 6,571,083 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a59075f2ecd60fedcb58e373d79655510c18f270b46f8230851779bd9eed06a7

View on Chainz ↗

Height

#225,407

Difficulty

9.936746

Transactions

Size

652 B

Version

Bits

09efce93

Nonce

110,381

Timestamp

10/24/2013, 11:17:01 AM

Confirmations

6,571,083

Mined by

⛏️ P2SHARD9nP5VZzTxnyC1DV6HtceziVTKFm3wGi

Merkle Root

76e167d3db95abe7299688ead5a38d0cd2448b68e7c2dc6eca247492f439057d

Transactions (3)

Coinbasec56fafac9289a9…3199d5396582a6

1 in → 1 out10.1300 XPM109 B

ARD9nP5V…TKFm3wGi

54404218c1775c…26b6150c33403b

1 in → 2 out10.1000 XPM226 B

ATVsD4wh…iNZG78Vg AaYBJ5QB…D82bB7Rd

f273ae74d07e40…19d02b4695b71c

1 in → 2 out10.1000 XPM226 B

AUgnY9ii…PJXP8hbK AYuDpxGi…ggqqz7vu

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.

1.187 × 10⁹⁷(98-digit number)

11872565162813512069…46370659687922972159

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

1.187 × 10⁹⁷(98-digit number)

11872565162813512069…46370659687922972159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.187 × 10⁹⁷(98-digit number)

11872565162813512069…46370659687922972161

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

2.374 × 10⁹⁷(98-digit number)

23745130325627024138…92741319375845944319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.374 × 10⁹⁷(98-digit number)

23745130325627024138…92741319375845944321

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

4.749 × 10⁹⁷(98-digit number)

47490260651254048277…85482638751691888639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.749 × 10⁹⁷(98-digit number)

47490260651254048277…85482638751691888641

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

9.498 × 10⁹⁷(98-digit number)

94980521302508096554…70965277503383777279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.498 × 10⁹⁷(98-digit number)

94980521302508096554…70965277503383777281

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

1.899 × 10⁹⁸(99-digit number)

18996104260501619310…41930555006767554559

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