Block #273,091

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 3:08:34 PM · Difficulty 9.9540 · 6,534,493 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4cf00140c9b743a43d1ed8efb0fb18296e1aac25f99b50432f11f46b468ce226

View on Chainz ↗

Height

#273,091

Difficulty

9.953964

Transactions

Size

1.27 KB

Version

Bits

09f43703

Nonce

13,821

Timestamp

11/25/2013, 3:08:34 PM

Confirmations

6,534,493

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

1195d59cb098620185043350efbe4040ae5d9b3ccedb007251c60c607ab33a0c

Transactions (5)

Coinbase5238f87e439ac2…13a01d0cd0f9d2

1 in → 2 out10.1200 XPM140 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

aa7418114d9490…20b6f7f1e6e83b

2 in → 1 out20.1600 XPM273 B

AHpZvKXh…psFtnf1m

261037504560b9…18530d263592ad

1 in → 1 out3.2157 XPM191 B

AbjtpDHw…mMmabF9W

0071153f6fe163…8be5cd6d119beb

1 in → 2 out1.3993 XPM226 B

AFsk8Py3…poueJDWt AGdU3418…h2yBWXQe

eeeceaab119b5e…5be64113b4a0f5

2 in → 2 out0.3388 XPM374 B

AFsk8Py3…poueJDWt AewU48Xy…Xky8YW1A

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.

7.145 × 10¹⁰⁴(105-digit number)

71453253025323968260…48919037645730885119

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

7.145 × 10¹⁰⁴(105-digit number)

71453253025323968260…48919037645730885119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.145 × 10¹⁰⁴(105-digit number)

71453253025323968260…48919037645730885121

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

1.429 × 10¹⁰⁵(106-digit number)

14290650605064793652…97838075291461770239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.429 × 10¹⁰⁵(106-digit number)

14290650605064793652…97838075291461770241

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

2.858 × 10¹⁰⁵(106-digit number)

28581301210129587304…95676150582923540479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.858 × 10¹⁰⁵(106-digit number)

28581301210129587304…95676150582923540481

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

5.716 × 10¹⁰⁵(106-digit number)

57162602420259174608…91352301165847080959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.716 × 10¹⁰⁵(106-digit number)

57162602420259174608…91352301165847080961

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

1.143 × 10¹⁰⁶(107-digit number)

11432520484051834921…82704602331694161919

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 #273,091

Cookie Preferences