Block #471,166

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 10:10:45 AM · Difficulty 10.4313 · 6,341,314 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f1bfe55e4fbdd953272002f7efa7bd2ba0807d29f7635ac16023849aa9874ce4

View on Chainz ↗

Height

#471,166

Difficulty

10.431309

Transactions

Size

905 B

Version

Bits

0a6e6a41

Nonce

274,562

Timestamp

4/2/2014, 10:10:45 AM

Confirmations

6,341,314

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

51cc60d2d094f0a5f8fa147da423465c8e4ba85771744ac5e8e21aa038226621

Transactions (1)

Coinbase51cc60d2d094f0…e21aa038226621

1 in → 22 out9.1800 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AZ34NcPy…8FPeFjPV Adbb4svj…dQWTHsq5 ATp4jJhs…TbSgR8Qb

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.

1.033 × 10¹⁰⁴(105-digit number)

10337960449576823501…44636934578083522559

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

1.033 × 10¹⁰⁴(105-digit number)

10337960449576823501…44636934578083522559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.033 × 10¹⁰⁴(105-digit number)

10337960449576823501…44636934578083522561

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

2.067 × 10¹⁰⁴(105-digit number)

20675920899153647003…89273869156167045119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.067 × 10¹⁰⁴(105-digit number)

20675920899153647003…89273869156167045121

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

4.135 × 10¹⁰⁴(105-digit number)

41351841798307294007…78547738312334090239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.135 × 10¹⁰⁴(105-digit number)

41351841798307294007…78547738312334090241

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

8.270 × 10¹⁰⁴(105-digit number)

82703683596614588015…57095476624668180479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.270 × 10¹⁰⁴(105-digit number)

82703683596614588015…57095476624668180481

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

1.654 × 10¹⁰⁵(106-digit number)

16540736719322917603…14190953249336360959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.654 × 10¹⁰⁵(106-digit number)

16540736719322917603…14190953249336360961

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 #471,166

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