Block #538,378

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/12/2014, 7:20:48 AM · Difficulty 10.9213 · 6,269,066 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53ed17b62be0764be286917a2c025d0a701c818aeb45e4594b71e52c059671ba

View on Chainz ↗

Height

#538,378

Difficulty

10.921266

Transactions

Size

732 B

Version

Bits

0aebd814

Nonce

77,589

Timestamp

5/12/2014, 7:20:48 AM

Confirmations

6,269,066

Mined by

⛏️ 7aSpv%AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e611689924474bac8711bc6270bbd87bf782338295115bbd5b71fca58f6dd555

Transactions (1)

Coinbasee611689924474b…71fca58f6dd555

1 in → 17 out8.3700 XPM641 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

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.

2.569 × 10⁹⁶(97-digit number)

25693174904044417659…13147764927445031999

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

2.569 × 10⁹⁶(97-digit number)

25693174904044417659…13147764927445031999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.569 × 10⁹⁶(97-digit number)

25693174904044417659…13147764927445032001

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

5.138 × 10⁹⁶(97-digit number)

51386349808088835319…26295529854890063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.138 × 10⁹⁶(97-digit number)

51386349808088835319…26295529854890064001

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

1.027 × 10⁹⁷(98-digit number)

10277269961617767063…52591059709780127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.027 × 10⁹⁷(98-digit number)

10277269961617767063…52591059709780128001

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

2.055 × 10⁹⁷(98-digit number)

20554539923235534127…05182119419560255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.055 × 10⁹⁷(98-digit number)

20554539923235534127…05182119419560256001

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

4.110 × 10⁹⁷(98-digit number)

41109079846471068255…10364238839120511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.110 × 10⁹⁷(98-digit number)

41109079846471068255…10364238839120512001

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

8.221 × 10⁹⁷(98-digit number)

82218159692942136510…20728477678241023999

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 #538,378

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