Block #477,896

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 5:55:52 PM · Difficulty 10.4885 · 6,334,755 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

932963f18ed30e1433d1f19e2737d4d618e7b770e7fff49e9bb7f211e648c03a

View on Chainz ↗

Height

#477,896

Difficulty

10.488531

Transactions

Size

3.35 KB

Version

Bits

0a7d1065

Nonce

294,236

Timestamp

4/6/2014, 5:55:52 PM

Confirmations

6,334,755

Mined by

⛏️ JAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

5b6abb9ca428619b349a2132ffaafa7afcc56cd43ce813687bc3cbd9f16f697c

Transactions (5)

Coinbaseaa442559b124b3…36021458ce500b

1 in → 22 out9.1300 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AUFKXvnz…342ApNcm AdoqUYAy…tJ482T9b

b5e979a1a63009…f072d82bdcfd02

12 in → 2 out36.1618 XPM1.81 KB

AMwQ2ew3…WhZsngQu AQKAGG7g…oMSPNQMo

e0521652b549b2…e34d38fb16adf8

1 in → 2 out8.1298 XPM226 B

ASc7b8wj…B5FHYVmu AaYc3Kop…9ufpGLeL

aa7fb65aa79591…0f5fd9e0380af0

1 in → 2 out8.1207 XPM226 B

AGz5ycfC…gmvHMXuj Ae9UPc8D…SDX1kyju

16ee7dd46a9a26…7b4c6011a11f6f

1 in → 2 out7.1072 XPM227 B

AZDUEbdS…RYKMRZET AXBP3UFK…gWKtBiyK

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.

1.378 × 10⁹³(94-digit number)

13787943966656951598…12260204602889379959

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

1.378 × 10⁹³(94-digit number)

13787943966656951598…12260204602889379959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.378 × 10⁹³(94-digit number)

13787943966656951598…12260204602889379961

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

2.757 × 10⁹³(94-digit number)

27575887933313903196…24520409205778759919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.757 × 10⁹³(94-digit number)

27575887933313903196…24520409205778759921

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

5.515 × 10⁹³(94-digit number)

55151775866627806393…49040818411557519839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.515 × 10⁹³(94-digit number)

55151775866627806393…49040818411557519841

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

1.103 × 10⁹⁴(95-digit number)

11030355173325561278…98081636823115039679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.103 × 10⁹⁴(95-digit number)

11030355173325561278…98081636823115039681

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

2.206 × 10⁹⁴(95-digit number)

22060710346651122557…96163273646230079359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.206 × 10⁹⁴(95-digit number)

22060710346651122557…96163273646230079361

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 #477,896

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