Block #455,526

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 2:55:50 PM · Difficulty 10.4119 · 6,347,176 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50732231f50d39237197e63a94c0b5fca96921a920ed1c137aba858b28a40271

View on Chainz ↗

Height

#455,526

Difficulty

10.411900

Transactions

Size

5.84 KB

Version

Bits

0a69724e

Nonce

300,499

Timestamp

3/22/2014, 2:55:50 PM

Confirmations

6,347,176

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

378e95631fb4115901175ae76ae9653956223ce0a0b643945a3b60e6ba7ced09

Transactions (3)

Coinbaseb8c85adfd9e001…d87ef0dd7ddf4a

1 in → 1 out9.2800 XPM110 B

AeKNrjNj…1NEq95Ta

446914a2018a03…3b18cbee6d583c

13 in → 2 out39.7117 XPM1.96 KB

AYTrboja…JdbXeGRz AaiAPx6i…Afi8cQjQ

4325dddf6ce69c…88e5cfb64e029c

25 in → 2 out114.7235 XPM3.69 KB

AN1Tm8m9…suwySgLN AUm3GFiY…sCnf2z48

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.

5.126 × 10⁹⁸(99-digit number)

51267490789067791717…39282828684104372479

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

5.126 × 10⁹⁸(99-digit number)

51267490789067791717…39282828684104372479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.126 × 10⁹⁸(99-digit number)

51267490789067791717…39282828684104372481

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

1.025 × 10⁹⁹(100-digit number)

10253498157813558343…78565657368208744959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.025 × 10⁹⁹(100-digit number)

10253498157813558343…78565657368208744961

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

2.050 × 10⁹⁹(100-digit number)

20506996315627116687…57131314736417489919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.050 × 10⁹⁹(100-digit number)

20506996315627116687…57131314736417489921

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

4.101 × 10⁹⁹(100-digit number)

41013992631254233374…14262629472834979839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.101 × 10⁹⁹(100-digit number)

41013992631254233374…14262629472834979841

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

8.202 × 10⁹⁹(100-digit number)

82027985262508466748…28525258945669959679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.202 × 10⁹⁹(100-digit number)

82027985262508466748…28525258945669959681

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