Block #461,636

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 9:04:36 PM · Difficulty 10.4141 · 6,348,479 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cee621f5eb57716dc38a29890b21c8c21d85c1568b0d0b56f5ae9b74e4c9c138

View on Chainz ↗

Height

#461,636

Difficulty

10.414081

Transactions

Size

1.08 KB

Version

Bits

0a6a0138

Nonce

300,487,710

Timestamp

3/26/2014, 9:04:36 PM

Confirmations

6,348,479

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9a792a855407e4f52f1e7cb493336f35f8e40ccf82d20add375a6831554e54f1

Transactions (5)

Coinbase4f80d64832ca68…d6deca29f83a18

1 in → 1 out9.2500 XPM116 B

AbwWkWZt…kawDhufa

01648f97bab12e…7cdf9fc61564cb

1 in → 2 out9.1900 XPM225 B

AYfs53zD…GPbbNcmW AHkhdgvV…BZthedsa

7cc45f4acf6fd8…6f4f8bd21c90ab

1 in → 2 out9.1900 XPM226 B

AZjZDSEF…NgCip2nu ALNcqvrc…pcJVqv18

9d81273aa53edf…a344394f759689

1 in → 2 out9.1800 XPM225 B

APRFwjru…mxxXUjhH AYFxzicp…jeAdgy2P

d4b4543eaa6bd1…759c8d0bda3363

1 in → 2 out9.1800 XPM225 B

AHDArqQW…nNZMgWAb ALTyK1qW…HeRV1nBW

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.

9.046 × 10⁹⁷(98-digit number)

90460067964355781459…18842381410903860479

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

9.046 × 10⁹⁷(98-digit number)

90460067964355781459…18842381410903860479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.046 × 10⁹⁷(98-digit number)

90460067964355781459…18842381410903860481

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

1.809 × 10⁹⁸(99-digit number)

18092013592871156291…37684762821807720959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.809 × 10⁹⁸(99-digit number)

18092013592871156291…37684762821807720961

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

3.618 × 10⁹⁸(99-digit number)

36184027185742312583…75369525643615441919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.618 × 10⁹⁸(99-digit number)

36184027185742312583…75369525643615441921

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

7.236 × 10⁹⁸(99-digit number)

72368054371484625167…50739051287230883839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.236 × 10⁹⁸(99-digit number)

72368054371484625167…50739051287230883841

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

1.447 × 10⁹⁹(100-digit number)

14473610874296925033…01478102574461767679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.447 × 10⁹⁹(100-digit number)

14473610874296925033…01478102574461767681

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 #461,636

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