Block #472,948

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 2:21:23 PM · Difficulty 10.4425 · 6,330,652 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a60740e72750fc3e89a6722cd1ddc513c3a0585969ae2519f883b2ab261a105

View on Chainz ↗

Height

#472,948

Difficulty

10.442505

Transactions

Size

622 B

Version

Bits

0a7147fe

Nonce

361,819

Timestamp

4/3/2014, 2:21:23 PM

Confirmations

6,330,652

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2a106b91ab0dca4968434850bd628b692af4aff63d90299ae97554bd2e4d40ea

Transactions (3)

Coinbase59ec0510838dba…21ad3657222ca8

1 in → 1 out9.1800 XPM110 B

AeKNrjNj…1NEq95Ta

6904c8b59f47fa…e55f07123e2b7e

1 in → 2 out711.2289 XPM227 B

AdB9X8g8…JX87QERW AaC5E2y2…L8gD82oL

2beb9eca03103c…e8f9d374b970b4

1 in → 1 out2.9901 XPM192 B

AJRaP3ni…DyH1EPUW

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.

2.003 × 10¹⁰²(103-digit number)

20031233052583047939…03995153201051024079

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

2.003 × 10¹⁰²(103-digit number)

20031233052583047939…03995153201051024079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.003 × 10¹⁰²(103-digit number)

20031233052583047939…03995153201051024081

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

4.006 × 10¹⁰²(103-digit number)

40062466105166095878…07990306402102048159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.006 × 10¹⁰²(103-digit number)

40062466105166095878…07990306402102048161

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

8.012 × 10¹⁰²(103-digit number)

80124932210332191757…15980612804204096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.012 × 10¹⁰²(103-digit number)

80124932210332191757…15980612804204096321

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

1.602 × 10¹⁰³(104-digit number)

16024986442066438351…31961225608408192639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.602 × 10¹⁰³(104-digit number)

16024986442066438351…31961225608408192641

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

3.204 × 10¹⁰³(104-digit number)

32049972884132876703…63922451216816385279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.204 × 10¹⁰³(104-digit number)

32049972884132876703…63922451216816385281

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