Block #271,321

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 1:40:31 PM · Difficulty 9.9517 · 6,528,212 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cb7d385c8600cb3217b606938ca5017d113755c00a8cfe87d2f369684f1e393

View on Chainz ↗

Height

#271,321

Difficulty

9.951732

Transactions

Size

1.71 KB

Version

Bits

09f3a4ad

Nonce

26,564

Timestamp

11/24/2013, 1:40:31 PM

Confirmations

6,528,212

Mined by

⛏️ #aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

db4845d2b58848bfb59fcab35c66559f989000b359a2bb8f77acd37ad78229dd

Transactions (4)

Coinbasea8cd841d655497…50f9d2b0a15cd9

1 in → 27 out10.0800 XPM981 B

APeshfYV…3PKcKMKH APVGazMT…cDCk2nwA ARanXFdq…2FNquU2w AQyr8Lw3…hs4nt3Pn ALFWpHxd…zhX7LjhL

4389eeae437fcf…967ded3024ea4b

1 in → 2 out10.0600 XPM226 B

Abyspbiu…iX9n961T APPyh5VV…CaqoUc7C

a80b44a3b19982…03f36ea431b10f

1 in → 2 out10.0600 XPM227 B

AKxSckFn…A7G6r1GF AHJZe99R…VN5agbar

842a3ac17dfc2a…4ee30dc84b4374

1 in → 2 out10.0600 XPM226 B

AeRCbdMR…MiuZWXdH AaVFHFSq…bCnX1Bpw

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.

1.658 × 10¹⁰⁰(101-digit number)

16584883653371545939…48131487840741232239

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

1.658 × 10¹⁰⁰(101-digit number)

16584883653371545939…48131487840741232239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.658 × 10¹⁰⁰(101-digit number)

16584883653371545939…48131487840741232241

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

3.316 × 10¹⁰⁰(101-digit number)

33169767306743091879…96262975681482464479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.316 × 10¹⁰⁰(101-digit number)

33169767306743091879…96262975681482464481

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

6.633 × 10¹⁰⁰(101-digit number)

66339534613486183759…92525951362964928959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.633 × 10¹⁰⁰(101-digit number)

66339534613486183759…92525951362964928961

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

1.326 × 10¹⁰¹(102-digit number)

13267906922697236751…85051902725929857919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.326 × 10¹⁰¹(102-digit number)

13267906922697236751…85051902725929857921

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

2.653 × 10¹⁰¹(102-digit number)

26535813845394473503…70103805451859715839

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