Block #462,669

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 2:17:35 PM · Difficulty 10.4153 · 6,351,721 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0eb3cd10d007ac4d047e39abf7743b8dedd309a567c76ff2a841f5a058c9f34

View on Chainz ↗

Height

#462,669

Difficulty

10.415318

Transactions

Size

1.31 KB

Version

Bits

0a6a524d

Nonce

154,596

Timestamp

3/27/2014, 2:17:35 PM

Confirmations

6,351,721

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

03afd66cbf3a1e0e01b503386146e3ba95ecea112d18f5ec5402fd7b0eaf125c

Transactions (2)

Coinbasebcc883ab7f2349…fe5d75f0022a10

1 in → 1 out9.2200 XPM110 B

AeKNrjNj…1NEq95Ta

6216a0b4aa767a…a8e21e6546331b

6 in → 10 out27.8157 XPM1.11 KB

AbpVB1nR…SWfdKu93 AbegGsha…RYQxrpFP AXsvaFWm…Jy7HiavE AHAPmauK…a5LvR1Xp AXDEZh15…FbrAPGkC

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.

5.335 × 10¹⁰⁰(101-digit number)

53352588006249268447…95347049589297306719

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

5.335 × 10¹⁰⁰(101-digit number)

53352588006249268447…95347049589297306719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.335 × 10¹⁰⁰(101-digit number)

53352588006249268447…95347049589297306721

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

1.067 × 10¹⁰¹(102-digit number)

10670517601249853689…90694099178594613439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.067 × 10¹⁰¹(102-digit number)

10670517601249853689…90694099178594613441

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

2.134 × 10¹⁰¹(102-digit number)

21341035202499707378…81388198357189226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.134 × 10¹⁰¹(102-digit number)

21341035202499707378…81388198357189226881

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

4.268 × 10¹⁰¹(102-digit number)

42682070404999414757…62776396714378453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.268 × 10¹⁰¹(102-digit number)

42682070404999414757…62776396714378453761

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

8.536 × 10¹⁰¹(102-digit number)

85364140809998829515…25552793428756907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.536 × 10¹⁰¹(102-digit number)

85364140809998829515…25552793428756907521

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 #462,669

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