Block #250,627

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 2:35:30 PM · Difficulty 9.9686 · 6,559,226 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc800f544fe643247fc2db080d250ffd9ce7e1fa092b17e7d65a4272d207a987

View on Chainz ↗

Height

#250,627

Difficulty

9.968640

Transactions

Size

2.48 KB

Version

Bits

09f7f8c3

Nonce

8,822

Timestamp

11/8/2013, 2:35:30 PM

Confirmations

6,559,226

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

9f7a065db1026c550fbfee307712679685377801a829b1eb8a18ba4e72e239f7

Transactions (5)

Coinbaseb190a7e3d928c6…d1bda1b5af1083

1 in → 2 out10.1000 XPM141 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

beb6f3f24e423b…17c0d9af2d508b

2 in → 2 out100.9227 XPM375 B

AQ996cWc…xquCW4MB APkzAv5n…VECD18aK

0dd7328ccb9e21…341bc822e9cdf8

1 in → 2 out10.0500 XPM227 B

ALrAyV4f…9n4Df2h2 AMsr9Rez…6CvbYSL9

ebd27bbe4cd621…e7a3374c35a5e8

7 in → 4 out9.2018 XPM1.15 KB

AVQ5uZUo…s7JZA7HP AbNgL8yS…Wu6nPFk5 AUfa5LFJ…C4BhhWGa AeKNrjNj…1NEq95Ta

732842399167fa…3aceaf22e8b83c

3 in → 2 out2.0395 XPM523 B

AXatm7Se…KGsBBnzt AVzEMaB2…MfXqkWVb

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.

1.333 × 10⁹⁴(95-digit number)

13333428165121366871…07084698306923050969

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

1.333 × 10⁹⁴(95-digit number)

13333428165121366871…07084698306923050969

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.333 × 10⁹⁴(95-digit number)

13333428165121366871…07084698306923050971

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

2.666 × 10⁹⁴(95-digit number)

26666856330242733743…14169396613846101939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.666 × 10⁹⁴(95-digit number)

26666856330242733743…14169396613846101941

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

5.333 × 10⁹⁴(95-digit number)

53333712660485467487…28338793227692203879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.333 × 10⁹⁴(95-digit number)

53333712660485467487…28338793227692203881

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

1.066 × 10⁹⁵(96-digit number)

10666742532097093497…56677586455384407759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.066 × 10⁹⁵(96-digit number)

10666742532097093497…56677586455384407761

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

2.133 × 10⁹⁵(96-digit number)

21333485064194186995…13355172910768815519

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 #250,627

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