Block #455,753

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 6:05:01 PM · Difficulty 10.4166 · 6,362,221 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67b73d5ee63e0277760104285c36e56a3ae498f4481d4a57c12b71c67d08bb02

View on Chainz ↗

Height

#455,753

Difficulty

10.416557

Transactions

Size

428 B

Version

Bits

0a6aa383

Nonce

47,722

Timestamp

3/22/2014, 6:05:01 PM

Confirmations

6,362,221

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a232bc2c434bc8bc4ffd795d8a292bf132014597e4b737c93fadeb592c798964

Transactions (2)

Coinbaseef239e5472a8ef…11ded1704dba7a

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

718e8012d5efb0…7ecdf5e019fd89

1 in → 2 out133.2781 XPM227 B

AHA9fN8X…KFsLBUfg AQjE7msA…V49aERCj

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.

1.070 × 10⁹⁶(97-digit number)

10700868182522883060…66233009564802903039

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

1.070 × 10⁹⁶(97-digit number)

10700868182522883060…66233009564802903039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.070 × 10⁹⁶(97-digit number)

10700868182522883060…66233009564802903041

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

2.140 × 10⁹⁶(97-digit number)

21401736365045766120…32466019129605806079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.140 × 10⁹⁶(97-digit number)

21401736365045766120…32466019129605806081

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

4.280 × 10⁹⁶(97-digit number)

42803472730091532241…64932038259211612159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.280 × 10⁹⁶(97-digit number)

42803472730091532241…64932038259211612161

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

8.560 × 10⁹⁶(97-digit number)

85606945460183064483…29864076518423224319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.560 × 10⁹⁶(97-digit number)

85606945460183064483…29864076518423224321

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

1.712 × 10⁹⁷(98-digit number)

17121389092036612896…59728153036846448639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.712 × 10⁹⁷(98-digit number)

17121389092036612896…59728153036846448641

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 #455,753

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