Block #249,911

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 5:30:29 AM · Difficulty 9.9675 · 6,556,795 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

700cf1686546c00c68dd8e7d19e26e3cef88a74349479100aa60e810136b60e1

View on Chainz ↗

Height

#249,911

Difficulty

9.967545

Transactions

Size

682 B

Version

Bits

09f7b106

Nonce

31,803

Timestamp

11/8/2013, 5:30:29 AM

Confirmations

6,556,795

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

e1d0dccf6290769bd1dd21e3656bb581e7add2652ce5eec130daa1d9ebb0edd0

Transactions (3)

Coinbase62aad54a80f855…c72d2954963285

1 in → 2 out10.0700 XPM141 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

679e43b9caf9a3…32f820106fb7ee

1 in → 2 out8.0015 XPM226 B

AXM549xw…a6pNkFPX AQ3iUWMY…Qtq93StD

d2a0044c165e5f…fac15c0d10d44c

1 in → 2 out5.2623 XPM225 B

AJbzvFJR…sNT5VjB7 AabeYMkc…rYY6UYYH

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.

2.796 × 10⁹⁴(95-digit number)

27968903907442240256…89901691738288181559

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

2.796 × 10⁹⁴(95-digit number)

27968903907442240256…89901691738288181559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.796 × 10⁹⁴(95-digit number)

27968903907442240256…89901691738288181561

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

5.593 × 10⁹⁴(95-digit number)

55937807814884480512…79803383476576363119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.593 × 10⁹⁴(95-digit number)

55937807814884480512…79803383476576363121

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

1.118 × 10⁹⁵(96-digit number)

11187561562976896102…59606766953152726239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.118 × 10⁹⁵(96-digit number)

11187561562976896102…59606766953152726241

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

2.237 × 10⁹⁵(96-digit number)

22375123125953792205…19213533906305452479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.237 × 10⁹⁵(96-digit number)

22375123125953792205…19213533906305452481

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

4.475 × 10⁹⁵(96-digit number)

44750246251907584410…38427067812610904959

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 #249,911

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