Block #472,546

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 8:33:56 AM · Difficulty 10.4361 · 6,338,435 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a522e03780836763e190baf69d100f287d04565e75d8c020770dbf3ab859ea4

View on Chainz ↗

Height

#472,546

Difficulty

10.436094

Transactions

Size

65.45 KB

Version

Bits

0a6fa3e0

Nonce

9,433

Timestamp

4/3/2014, 8:33:56 AM

Confirmations

6,338,435

Mined by

⛏️ P2SHAZeU2g2L3DVc23NKBGDPLkL6PBm694WpGV

Merkle Root

05f5b7afbbad536895a476f1db9a8ebded77f42b388c16d46f28f1865ed4655a

Transactions (4)

Coinbase7a80f1e12f33c4…827ca997011092

1 in → 1 out9.8620 XPM111 B

AZeU2g2L…m694WpGV

67a0aeb7401055…ae8c6b63ff8b3a

1 in → 2 out365.0889 XPM227 B

AWuSCNAy…MB1fRPQg AdweRjWJ…dRkehUrg

c45da79f1b8143…26e3a4e12e89c7

4 in → 1 out3.9900 XPM635 B

AVsbEYcQ…E758QYsw

089454c9a4adb6…25fd9b37e9e30d

445 in → 2 out150.2213 XPM64.41 KB

AQ3W6QHC…24n8B6hL AZYGkGKF…7DYMw8eQ

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.

1.077 × 10⁹⁵(96-digit number)

10778503825105877950…57158495538915177599

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

1.077 × 10⁹⁵(96-digit number)

10778503825105877950…57158495538915177599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.077 × 10⁹⁵(96-digit number)

10778503825105877950…57158495538915177601

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

2.155 × 10⁹⁵(96-digit number)

21557007650211755901…14316991077830355199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.155 × 10⁹⁵(96-digit number)

21557007650211755901…14316991077830355201

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

4.311 × 10⁹⁵(96-digit number)

43114015300423511803…28633982155660710399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.311 × 10⁹⁵(96-digit number)

43114015300423511803…28633982155660710401

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

8.622 × 10⁹⁵(96-digit number)

86228030600847023606…57267964311321420799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.622 × 10⁹⁵(96-digit number)

86228030600847023606…57267964311321420801

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

1.724 × 10⁹⁶(97-digit number)

17245606120169404721…14535928622642841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.724 × 10⁹⁶(97-digit number)

17245606120169404721…14535928622642841601

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 #472,546

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