Block #450,662

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2014, 10:34:07 AM · Difficulty 10.3752 · 6,367,239 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

57abcf0022facc10fb7e07c7ed115e2eadd41463cbaf35b580146b0c015a1087

View on Chainz ↗

Height

#450,662

Difficulty

10.375155

Transactions

Size

1012 B

Version

Bits

0a600a2b

Nonce

154,794

Timestamp

3/19/2014, 10:34:07 AM

Confirmations

6,367,239

Mined by

⛏️ faSANEZwy9tw1DgYw4uGbmja8PNbrE1uf5dKY

Merkle Root

a16c4a6dd9ac4b89dacde85b708938c8e6cbde4ca454054e6fa3eee34b7c4dc8

Transactions (4)

Coinbase55c61c31dd5d5b…465a3da2836b9b

1 in → 1 out9.2800 XPM97 B

ANEZwy9t…E1uf5dKY

192ec4b4f999a8…f9bdccf123cab2

2 in → 2 out14.5071 XPM375 B

AM9gxnSA…EBSVq4PJ AeMzqPGF…dHiY7mFe

09be1421ff1aaf…1c2de9e01a643d

1 in → 2 out7.2555 XPM225 B

ASThWgEr…fjBGN7vK AcEwBoZe…6229N7gJ

c3bdd72e3b5f3a…5e41377a1ff043

1 in → 2 out5.1566 XPM226 B

AbkyZsvA…G8VErJsN AZvosvzF…9GyKiY7W

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.

3.266 × 10⁹¹(92-digit number)

32664846821783733128…04493459453205295359

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

3.266 × 10⁹¹(92-digit number)

32664846821783733128…04493459453205295359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.266 × 10⁹¹(92-digit number)

32664846821783733128…04493459453205295361

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

6.532 × 10⁹¹(92-digit number)

65329693643567466256…08986918906410590719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.532 × 10⁹¹(92-digit number)

65329693643567466256…08986918906410590721

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

1.306 × 10⁹²(93-digit number)

13065938728713493251…17973837812821181439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.306 × 10⁹²(93-digit number)

13065938728713493251…17973837812821181441

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

2.613 × 10⁹²(93-digit number)

26131877457426986502…35947675625642362879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.613 × 10⁹²(93-digit number)

26131877457426986502…35947675625642362881

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

5.226 × 10⁹²(93-digit number)

52263754914853973005…71895351251284725759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.226 × 10⁹²(93-digit number)

52263754914853973005…71895351251284725761

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 #450,662

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