Block #294,956

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 4:33:09 AM · Difficulty 9.9912 · 6,508,462 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ccfcb93ce5833786e284116c866ae2a794b134928408e179d25b9e83db7a86f7

View on Chainz ↗

Height

#294,956

Difficulty

9.991176

Transactions

Size

2.53 KB

Version

Bits

09fdbdbb

Nonce

143,829

Timestamp

12/5/2013, 4:33:09 AM

Confirmations

6,508,462

Mined by

⛏️ ,aR:AHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

4cef061e7cca746f4910899b824b5cd9cc0a7730ff3a217272da72a261295f10

Transactions (4)

Coinbase4e777056865a3e…d7cf8e860f10da

1 in → 30 out9.9800 XPM1.06 KB

AHuJ9wYh…BGmgHrKZ ARcqMJhp…RVLToQ6S AaPASCNm…8mfBVejh AY4LyZBe…7DTvswxY AXX2MCBh…Q97G5hHt

785ba3410ebd69…36852716de876b

6 in → 2 out1000.0130 XPM966 B

AKyxUt9j…eTm6QUYZ ATTDwyK6…nhV8EcAX

8a605f7662bcec…58ed739ef37a57

1 in → 2 out9.9900 XPM226 B

AJ4jR3kk…ZHGc24EJ AQ3X2VZb…inCyY6Rn

7fddd862925a05…9ab2c872bd8661

1 in → 2 out9.9900 XPM227 B

Abj8hi7q…F23VFNDF AGVw8RB1…mPdariVX

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.

1.417 × 10⁹³(94-digit number)

14175846451948876762…75216689950216339199

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

1.417 × 10⁹³(94-digit number)

14175846451948876762…75216689950216339199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.417 × 10⁹³(94-digit number)

14175846451948876762…75216689950216339201

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

2.835 × 10⁹³(94-digit number)

28351692903897753524…50433379900432678399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.835 × 10⁹³(94-digit number)

28351692903897753524…50433379900432678401

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

5.670 × 10⁹³(94-digit number)

56703385807795507048…00866759800865356799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.670 × 10⁹³(94-digit number)

56703385807795507048…00866759800865356801

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

1.134 × 10⁹⁴(95-digit number)

11340677161559101409…01733519601730713599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.134 × 10⁹⁴(95-digit number)

11340677161559101409…01733519601730713601

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

2.268 × 10⁹⁴(95-digit number)

22681354323118202819…03467039203461427199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.268 × 10⁹⁴(95-digit number)

22681354323118202819…03467039203461427201

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