Block #323,832

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/21/2013, 10:04:26 PM · Difficulty 10.2075 · 6,492,843 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c48e2920f3fd644d908b1c0045b7e7a5c4ede5ab266cf67259cbebe20fe08228

View on Chainz ↗

Height

#323,832

Difficulty

10.207494

Transactions

Size

1.08 KB

Version

Bits

0a351e55

Nonce

74,026

Timestamp

12/21/2013, 10:04:26 PM

Confirmations

6,492,843

Mined by

⛏️ aRQAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

11057336936c47fb9db02786ccfcb010821317eda6492567de4b193c32ef99b1

Transactions (1)

Coinbase11057336936c47…4b193c32ef99b1

1 in → 28 out9.5600 XPM1014 B

AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AJzWx2VD…j4ZSMit5

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.

7.318 × 10⁹⁷(98-digit number)

73189414784597669715…51278767985960169439

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

7.318 × 10⁹⁷(98-digit number)

73189414784597669715…51278767985960169439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.318 × 10⁹⁷(98-digit number)

73189414784597669715…51278767985960169441

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

1.463 × 10⁹⁸(99-digit number)

14637882956919533943…02557535971920338879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.463 × 10⁹⁸(99-digit number)

14637882956919533943…02557535971920338881

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

2.927 × 10⁹⁸(99-digit number)

29275765913839067886…05115071943840677759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.927 × 10⁹⁸(99-digit number)

29275765913839067886…05115071943840677761

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

5.855 × 10⁹⁸(99-digit number)

58551531827678135772…10230143887681355519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.855 × 10⁹⁸(99-digit number)

58551531827678135772…10230143887681355521

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

1.171 × 10⁹⁹(100-digit number)

11710306365535627154…20460287775362711039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.171 × 10⁹⁹(100-digit number)

11710306365535627154…20460287775362711041

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

2.342 × 10⁹⁹(100-digit number)

23420612731071254308…40920575550725422079

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 #323,832

Cookie Preferences