Block #250,737

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 3:51:31 PM · Difficulty 9.9689 · 6,565,960 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5568f380ad728ab93ead6bdb34822f3c767139e3399065e7c355a5ed30e5037e

View on Chainz ↗

Height

#250,737

Difficulty

9.968860

Transactions

Size

3.05 KB

Version

Bits

09f8073a

Nonce

5,820

Timestamp

11/8/2013, 3:51:31 PM

Confirmations

6,565,960

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

25873b77fe659ec03613004d593e6a71499da5e9abb2b184f263152276667573

Transactions (3)

Coinbase5e2e3b39c75202…c508ee53a44fc9

1 in → 2 out10.0800 XPM136 B

AZDUEbdS…RYKMRZET AU6kq4CL…dQBLvxLp

2fe6501cf789d8…0ecff84fdf5665

13 in → 1 out2.8058 XPM1.92 KB

AKfJihTE…izgEYet1

a00cd77569eb32…a3b590d073084c

6 in → 1 out0.7512 XPM933 B

APug1zqH…wfikf34c

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.

1.021 × 10⁹⁷(98-digit number)

10211064344131778124…22632969431258147839

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

1.021 × 10⁹⁷(98-digit number)

10211064344131778124…22632969431258147839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.021 × 10⁹⁷(98-digit number)

10211064344131778124…22632969431258147841

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

2.042 × 10⁹⁷(98-digit number)

20422128688263556249…45265938862516295679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.042 × 10⁹⁷(98-digit number)

20422128688263556249…45265938862516295681

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

4.084 × 10⁹⁷(98-digit number)

40844257376527112498…90531877725032591359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.084 × 10⁹⁷(98-digit number)

40844257376527112498…90531877725032591361

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

8.168 × 10⁹⁷(98-digit number)

81688514753054224997…81063755450065182719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.168 × 10⁹⁷(98-digit number)

81688514753054224997…81063755450065182721

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

1.633 × 10⁹⁸(99-digit number)

16337702950610844999…62127510900130365439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.633 × 10⁹⁸(99-digit number)

16337702950610844999…62127510900130365441

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 #250,737

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