Block #468,875

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 7:35:36 PM · Difficulty 10.4323 · 6,348,833 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aff863c78e3d62557350a3e7094b232789c43fab620c23d50f1d177c569c0834

View on Chainz ↗

Height

#468,875

Difficulty

10.432317

Transactions

Size

1.71 KB

Version

Bits

0a6eac59

Nonce

7,144

Timestamp

3/31/2014, 7:35:36 PM

Confirmations

6,348,833

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5736ae6cd97593c532e1b40cb71210ce8870e019d7ddcb8f722b38fdc4ef3d30

Transactions (3)

Coinbasea19281539c11ae…be8cdab76c0181

1 in → 1 out9.2069 XPM116 B

AbwWkWZt…kawDhufa

20926300a442db…833bc56b4891e0

5 in → 14 out46.1200 XPM1.03 KB

AZPAr1b2…Wk57bUEH AWmgpRJr…1uLevJJr AcpjiZSC…TNRJHCGa AQufhWCK…onJSt1Rt AcacZaAu…7XaX5VD6

d69cc172c0e05b…676fbc9caded5b

3 in → 1 out3.4100 XPM489 B

AUC8qpT3…zzD6FZvv

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.

3.384 × 10⁹⁹(100-digit number)

33844218487957045330…83867904351541132799

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

3.384 × 10⁹⁹(100-digit number)

33844218487957045330…83867904351541132799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.384 × 10⁹⁹(100-digit number)

33844218487957045330…83867904351541132801

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

6.768 × 10⁹⁹(100-digit number)

67688436975914090661…67735808703082265599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.768 × 10⁹⁹(100-digit number)

67688436975914090661…67735808703082265601

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

1.353 × 10¹⁰⁰(101-digit number)

13537687395182818132…35471617406164531199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.353 × 10¹⁰⁰(101-digit number)

13537687395182818132…35471617406164531201

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

2.707 × 10¹⁰⁰(101-digit number)

27075374790365636264…70943234812329062399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.707 × 10¹⁰⁰(101-digit number)

27075374790365636264…70943234812329062401

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

5.415 × 10¹⁰⁰(101-digit number)

54150749580731272528…41886469624658124799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.415 × 10¹⁰⁰(101-digit number)

54150749580731272528…41886469624658124801

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 #468,875

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