Block #225,417

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/24/2013, 11:33:01 AM · Difficulty 9.9367 · 6,568,898 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

390ef86919869060940c8d7f44af8fa3a7b32ca66c37002d1cb23b10134b37f0

View on Chainz ↗

Height

#225,417

Difficulty

9.936679

Transactions

Size

427 B

Version

Bits

09efca2b

Nonce

1,100

Timestamp

10/24/2013, 11:33:01 AM

Confirmations

6,568,898

Merkle Root

07a94d60768ffbceaca1d6cb091ecf8e77ca3629619d002bc74bcb5aced46b94

Transactions (2)

Coinbasefb546fd8ed5b61…b3d95a64f27ee7

1 in → 1 out10.1200 XPM109 B

AMRwGW7y…csx6b59v

bae90f0d3cf79e…7d9a9dcb28be4c

1 in → 2 out10.1000 XPM227 B

ARdEFcSb…mQoSgqJL ASfnshun…oiZ9KX3R

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.

3.201 × 10⁹⁷(98-digit number)

32012786255542046062…26643754155069276159

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

3.201 × 10⁹⁷(98-digit number)

32012786255542046062…26643754155069276159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.201 × 10⁹⁷(98-digit number)

32012786255542046062…26643754155069276161

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

6.402 × 10⁹⁷(98-digit number)

64025572511084092124…53287508310138552319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.402 × 10⁹⁷(98-digit number)

64025572511084092124…53287508310138552321

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

1.280 × 10⁹⁸(99-digit number)

12805114502216818424…06575016620277104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.280 × 10⁹⁸(99-digit number)

12805114502216818424…06575016620277104641

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

2.561 × 10⁹⁸(99-digit number)

25610229004433636849…13150033240554209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.561 × 10⁹⁸(99-digit number)

25610229004433636849…13150033240554209281

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

5.122 × 10⁹⁸(99-digit number)

51220458008867273699…26300066481108418559

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