Block #258,420

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 1:07:27 AM · Difficulty 9.9765 · 6,558,796 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b3e8ce39807f234e8fb4e7dcdb59b0c2deab79599cde163bb58f299a7e71ec8

View on Chainz ↗

Height

#258,420

Difficulty

9.976479

Transactions

Size

452 B

Version

Bits

09f9fa82

Nonce

24,220

Timestamp

11/13/2013, 1:07:27 AM

Confirmations

6,558,796

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

c54ea13c1167855bfb27b33427dc49cd6b9748991764d348b36be52dec6f073c

Transactions (2)

Coinbase177292a6a267b7…80038eae37d838

1 in → 2 out10.0400 XPM137 B

AZDUEbdS…RYKMRZET ALfEGCwh…VawujfMm

8fffe30064ba6b…7a5a9acc60ad89

1 in → 2 out112.2600 XPM225 B

AK6L8YDA…3cgnPBnR AJGGVmzn…EgTcYFVR

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.

9.635 × 10⁹⁴(95-digit number)

96359824234107804596…35986644889677541599

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

9.635 × 10⁹⁴(95-digit number)

96359824234107804596…35986644889677541599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.635 × 10⁹⁴(95-digit number)

96359824234107804596…35986644889677541601

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

1.927 × 10⁹⁵(96-digit number)

19271964846821560919…71973289779355083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.927 × 10⁹⁵(96-digit number)

19271964846821560919…71973289779355083201

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

3.854 × 10⁹⁵(96-digit number)

38543929693643121838…43946579558710166399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.854 × 10⁹⁵(96-digit number)

38543929693643121838…43946579558710166401

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

7.708 × 10⁹⁵(96-digit number)

77087859387286243676…87893159117420332799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.708 × 10⁹⁵(96-digit number)

77087859387286243676…87893159117420332801

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

1.541 × 10⁹⁶(97-digit number)

15417571877457248735…75786318234840665599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.541 × 10⁹⁶(97-digit number)

15417571877457248735…75786318234840665601

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 #258,420

Cookie Preferences