Block #251,792

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 5:36:02 AM · Difficulty 9.9703 · 6,539,761 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5552c60c77ff51d8ee6ec4ac1a630b947990a52a000ae50919d5fb2b1e565f84

View on Chainz ↗

Height

#251,792

Difficulty

9.970293

Transactions

Size

1.34 KB

Version

Bits

09f86526

Nonce

29,173

Timestamp

11/9/2013, 5:36:02 AM

Confirmations

6,539,761

Merkle Root

ed60991e926704bc8f6935e3dfd75677c9d8aa270d5e2fb727cad7ca72b9887e

Transactions (3)

Coinbase3b53996c7d3286…09881b3611a0e2

1 in → 2 out10.0600 XPM141 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

23b4a1eb5145f8…20cb388893ae81

1 in → 4 out10.0400 XPM259 B

AdBg5KBk…HQqjgCFj AeKNrjNj…1NEq95Ta ARTJCDz1…oJ6Hi1d9 AcADmAoe…8iNnoMzB

132a1cefa9311c…a43aa1e4cf261c

5 in → 4 out8.0140 XPM884 B

AUYhRDe3…pPANQeY3 ASJHGLen…byv2NmHn ANqGPzQZ…XxwHco3T AZAYcqyP…Bf5uQ6gQ

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.

2.070 × 10⁹⁶(97-digit number)

20703244055443838585…49038637852060424759

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

2.070 × 10⁹⁶(97-digit number)

20703244055443838585…49038637852060424759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.070 × 10⁹⁶(97-digit number)

20703244055443838585…49038637852060424761

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

4.140 × 10⁹⁶(97-digit number)

41406488110887677171…98077275704120849519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.140 × 10⁹⁶(97-digit number)

41406488110887677171…98077275704120849521

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

8.281 × 10⁹⁶(97-digit number)

82812976221775354342…96154551408241699039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.281 × 10⁹⁶(97-digit number)

82812976221775354342…96154551408241699041

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

1.656 × 10⁹⁷(98-digit number)

16562595244355070868…92309102816483398079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.656 × 10⁹⁷(98-digit number)

16562595244355070868…92309102816483398081

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

3.312 × 10⁹⁷(98-digit number)

33125190488710141736…84618205632966796159

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