Block #271,323

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 1:43:27 PM · Difficulty 9.9517 · 6,524,141 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f2895ccac50d6a9e670423467176882e8d737cc75e8c9210ee72d36453cf9a3

View on Chainz ↗

Height

#271,323

Difficulty

9.951723

Transactions

Size

1.68 KB

Version

Bits

09f3a425

Nonce

104,073

Timestamp

11/24/2013, 1:43:27 PM

Confirmations

6,524,141

Mined by

⛏️ #aR<+APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

fb7e7e29df29007f478d099583225d1e3c7a32deab3fecc13e2115eae2716aa4

Transactions (4)

Coinbasefac3a02e1f8475…31ebcacfcb50ad

1 in → 26 out10.0800 XPM947 B

APeshfYV…3PKcKMKH APVGazMT…cDCk2nwA ARanXFdq…2FNquU2w ALdHh27b…XNbqrvPf AUVqfVq3…o3Yn1hbN

de32f63b8f32ec…8f7f805696369f

1 in → 2 out8.0491 XPM226 B

AKFzsPbj…eGZNxCJ4 AZcGvqwy…5nQ9xtPx

34d9052e5fc93f…76a3d09f874653

1 in → 2 out7.7930 XPM227 B

AJcwYxzt…ZjGtW5gq AZMESreZ…9pUTPPHF

38ae2a815aa6e1…9a83a77d2c4f4b

1 in → 2 out3.9895 XPM226 B

ATrA1osE…yb7M2bRz ASNAz3Tu…zwGMqLpa

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.

1.287 × 10⁹⁸(99-digit number)

12873580872087386578…75334546743856506879

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

1.287 × 10⁹⁸(99-digit number)

12873580872087386578…75334546743856506879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.287 × 10⁹⁸(99-digit number)

12873580872087386578…75334546743856506881

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

2.574 × 10⁹⁸(99-digit number)

25747161744174773156…50669093487713013759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.574 × 10⁹⁸(99-digit number)

25747161744174773156…50669093487713013761

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

5.149 × 10⁹⁸(99-digit number)

51494323488349546312…01338186975426027519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.149 × 10⁹⁸(99-digit number)

51494323488349546312…01338186975426027521

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

1.029 × 10⁹⁹(100-digit number)

10298864697669909262…02676373950852055039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.029 × 10⁹⁹(100-digit number)

10298864697669909262…02676373950852055041

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

2.059 × 10⁹⁹(100-digit number)

20597729395339818525…05352747901704110079

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