Block #839,983

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/4/2014, 7:51:33 PM · Difficulty 10.9744 · 5,968,490 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a3c2333e5cf07f60088fe938b0ebf29dafe482ce9b73321ff9d71f5e22f484da

View on Chainz ↗

Height

#839,983

Difficulty

10.974391

Transactions

Size

1.08 KB

Version

Bits

0af971b7

Nonce

346,143,849

Timestamp

12/4/2014, 7:51:33 PM

Confirmations

5,968,490

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cef3da60de9be86022eb43855134be2e0c6be8503476c00d06eb5403bc55b4a4

Transactions (5)

Coinbase0e63c9520317ef…afc890aa50e929

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

42e3cb5d6c0959…20144487259b4d

1 in → 2 out8.2700 XPM225 B

Acux6D1X…6ZVuzPDQ AWeFTqSF…usRDA3NM

0d5aec338069ce…3d522cb0cfef0c

1 in → 2 out8.2700 XPM226 B

AMTvqX3a…sxpwNFyf ALjGeWUU…q2iLtCkW

cdf48f921869f9…52544e87d81c7b

1 in → 2 out8.2700 XPM226 B

APzbSEvK…EjdANgQe AMoJsji6…a13Bp22Q

5cbf257118fca0…ff84d41cfd07a4

1 in → 2 out6.2937 XPM225 B

ALbf5N9W…GYASvfXu AG3TPGas…cJvesb2o

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.

1.372 × 10⁹⁸(99-digit number)

13729176030587843169…90268768861384867839

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

1.372 × 10⁹⁸(99-digit number)

13729176030587843169…90268768861384867839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.372 × 10⁹⁸(99-digit number)

13729176030587843169…90268768861384867841

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

2.745 × 10⁹⁸(99-digit number)

27458352061175686338…80537537722769735679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.745 × 10⁹⁸(99-digit number)

27458352061175686338…80537537722769735681

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

5.491 × 10⁹⁸(99-digit number)

54916704122351372677…61075075445539471359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.491 × 10⁹⁸(99-digit number)

54916704122351372677…61075075445539471361

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

1.098 × 10⁹⁹(100-digit number)

10983340824470274535…22150150891078942719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.098 × 10⁹⁹(100-digit number)

10983340824470274535…22150150891078942721

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

2.196 × 10⁹⁹(100-digit number)

21966681648940549070…44300301782157885439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.196 × 10⁹⁹(100-digit number)

21966681648940549070…44300301782157885441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.393 × 10⁹⁹(100-digit number)

43933363297881098141…88600603564315770879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #839,983

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