Block #327,225

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 9:49:28 AM · Difficulty 10.1770 · 6,489,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0aeffb24cbb8b18a538a355eb6bbf4094e0934f05e7873051bff84bc78174107

View on Chainz ↗

Height

#327,225

Difficulty

10.177017

Transactions

Size

1.24 KB

Version

Bits

0a2d50f6

Nonce

417,896

Timestamp

12/24/2013, 9:49:28 AM

Confirmations

6,489,434

Mined by

⛏️ 9aRXAQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

68327764833935ab019926dfa23ef7328b3cce5a4e936c97eb9f4bdd6585719f

Transactions (2)

Coinbase9d3305a0f2470a…1c86cf56ec734c

1 in → 26 out9.6400 XPM947 B

AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AP5UvYhU…vLTDwkdA AJzWx2VD…j4ZSMit5

fd6f7d88f4a84a…467a194166d5ee

1 in → 2 out539.9900 XPM227 B

AaxFBXL8…qXS24v3V AeDJXrrN…hfU9ChQG

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.

3.831 × 10⁹⁹(100-digit number)

38317125673338976352…02351785412962365919

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

3.831 × 10⁹⁹(100-digit number)

38317125673338976352…02351785412962365919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.831 × 10⁹⁹(100-digit number)

38317125673338976352…02351785412962365921

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

7.663 × 10⁹⁹(100-digit number)

76634251346677952704…04703570825924731839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.663 × 10⁹⁹(100-digit number)

76634251346677952704…04703570825924731841

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

1.532 × 10¹⁰⁰(101-digit number)

15326850269335590540…09407141651849463679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.532 × 10¹⁰⁰(101-digit number)

15326850269335590540…09407141651849463681

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

3.065 × 10¹⁰⁰(101-digit number)

30653700538671181081…18814283303698927359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.065 × 10¹⁰⁰(101-digit number)

30653700538671181081…18814283303698927361

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

6.130 × 10¹⁰⁰(101-digit number)

61307401077342362163…37628566607397854719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.130 × 10¹⁰⁰(101-digit number)

61307401077342362163…37628566607397854721

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

Block #327,225

Cookie Preferences