Block #225,394

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/24/2013, 11:01:43 AM · Difficulty 9.9368 · 6,582,577 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f7b5622dde85d1d5361351b9a83a4773f3a02bb26452124073f3b92e6df565c7

View on Chainz ↗

Height

#225,394

Difficulty

9.936771

Transactions

Size

20.44 KB

Version

Bits

09efd037

Nonce

108,878

Timestamp

10/24/2013, 11:01:43 AM

Confirmations

6,582,577

Mined by

⛏️ rpRhAPoSaKbzo9Kf5Ly2MEJvq4hV4dyRMHcUim

Merkle Root

3112e20e9dc47269a265aa06908e378b6eb9abc9b2b3545d5c8e787e78592ceb

Transactions (4)

Coinbasefbcc0f70a7e743…245d56fe50ecd8

1 in → 31 out10.0900 XPM1.09 KB

APoSaKbz…yRMHcUim ANuKx9Ke…wm7nrBRq ALFWpHxd…zhX7LjhL AKXeSXzu…yeuNjvhB ARpndEmc…Hg792kEk

bb1d5f3dbd574b…67e0312ee193c1

1 in → 2 out10.1000 XPM191 B

AFz9fXym…wh4UqpkL AWxhXv26…SwSS5Rv2

bdd0038e526821…1e7f46c6ec9808

1 in → 2 out10.1000 XPM226 B

AYRVNeRJ…tDqemJXP ALFZN5XA…rFYhncYN

75b963c4a8bd81…c5d562763eef0c

130 in → 2 out100.0100 XPM18.86 KB

AH4eoPpT…zKqjJNZq ALG7hNHE…GVtmhodq

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.

3.338 × 10⁹³(94-digit number)

33386380329707957795…07404894977688173439

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

3.338 × 10⁹³(94-digit number)

33386380329707957795…07404894977688173439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.338 × 10⁹³(94-digit number)

33386380329707957795…07404894977688173441

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

6.677 × 10⁹³(94-digit number)

66772760659415915590…14809789955376346879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.677 × 10⁹³(94-digit number)

66772760659415915590…14809789955376346881

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

1.335 × 10⁹⁴(95-digit number)

13354552131883183118…29619579910752693759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.335 × 10⁹⁴(95-digit number)

13354552131883183118…29619579910752693761

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

2.670 × 10⁹⁴(95-digit number)

26709104263766366236…59239159821505387519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.670 × 10⁹⁴(95-digit number)

26709104263766366236…59239159821505387521

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

5.341 × 10⁹⁴(95-digit number)

53418208527532732472…18478319643010775039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.341 × 10⁹⁴(95-digit number)

53418208527532732472…18478319643010775041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #225,394

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