Block #452,558

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/20/2014, 4:14:12 PM · Difficulty 10.3905 · 6,362,526 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fd610886eb8ed9c1f15ad2ea3a411655fc11c14f99f4a4fd1ffcb611510bf37

View on Chainz ↗

Height

#452,558

Difficulty

10.390457

Transactions

Size

868 B

Version

Bits

0a63f4fb

Nonce

1,497

Timestamp

3/20/2014, 4:14:12 PM

Confirmations

6,362,526

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

22ae1ad7b004cc8f669e2febd5e06b54c40723db6b1e3744345a1c247d209318

Transactions (1)

Coinbase22ae1ad7b004cc…5a1c247d209318

1 in → 21 out9.2500 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH ASgUri65…C7NLcyBg AcgDwGo8…BBFwbjVo

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.

5.426 × 10⁹⁷(98-digit number)

54268504356544602306…99169585183937378839

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

5.426 × 10⁹⁷(98-digit number)

54268504356544602306…99169585183937378839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.426 × 10⁹⁷(98-digit number)

54268504356544602306…99169585183937378841

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

1.085 × 10⁹⁸(99-digit number)

10853700871308920461…98339170367874757679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.085 × 10⁹⁸(99-digit number)

10853700871308920461…98339170367874757681

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

2.170 × 10⁹⁸(99-digit number)

21707401742617840922…96678340735749515359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.170 × 10⁹⁸(99-digit number)

21707401742617840922…96678340735749515361

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

4.341 × 10⁹⁸(99-digit number)

43414803485235681844…93356681471499030719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.341 × 10⁹⁸(99-digit number)

43414803485235681844…93356681471499030721

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

8.682 × 10⁹⁸(99-digit number)

86829606970471363689…86713362942998061439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.682 × 10⁹⁸(99-digit number)

86829606970471363689…86713362942998061441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.736 × 10⁹⁹(100-digit number)

17365921394094272737…73426725885996122879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #452,558

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