Block #2,635,858

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/29/2018, 9:29:36 AM · Difficulty 11.3445 · 4,200,608 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8849623ea0ce4ef183c158b14989a545b369d1efabb885e1362d5bd654765efc

View on Chainz ↗

Height

#2,635,858

Difficulty

11.344471

Transactions

Size

675 B

Version

Bits

0b582f43

Nonce

1,611,783,041

Timestamp

4/29/2018, 9:29:36 AM

Confirmations

4,200,608

Mined by

⛏️ P2SHASjkjW9fijfEsTyU2CeJtHuRu4sCBUM6Z8

Merkle Root

0da20ab185ce993e446d8b6671ba67bd27859c96f13c6206d2287e2a1a577819

Transactions (2)

Coinbase087070a7e543f8…3fc6d48a3fbdbf

1 in → 1 out7.7700 XPM110 B

ASjkjW9f…sCBUM6Z8

e11406fd98fa95…8e774f253892a5

2 in → 5 out393.3965 XPM476 B

ARznVePF…S7wvbB9s ASk9H3sY…qUG8r1d4 AKWi8GSY…nW1QsGMw APi8C85f…Lg5MDiei AScuzJcH…PXnbGC6h

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.

6.430 × 10⁹¹(92-digit number)

64300166792531369069…60419518187651788959

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

6.430 × 10⁹¹(92-digit number)

64300166792531369069…60419518187651788959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.430 × 10⁹¹(92-digit number)

64300166792531369069…60419518187651788961

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

1.286 × 10⁹²(93-digit number)

12860033358506273813…20839036375303577919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.286 × 10⁹²(93-digit number)

12860033358506273813…20839036375303577921

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

2.572 × 10⁹²(93-digit number)

25720066717012547627…41678072750607155839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.572 × 10⁹²(93-digit number)

25720066717012547627…41678072750607155841

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

5.144 × 10⁹²(93-digit number)

51440133434025095255…83356145501214311679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.144 × 10⁹²(93-digit number)

51440133434025095255…83356145501214311681

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

1.028 × 10⁹³(94-digit number)

10288026686805019051…66712291002428623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.028 × 10⁹³(94-digit number)

10288026686805019051…66712291002428623361

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

2.057 × 10⁹³(94-digit number)

20576053373610038102…33424582004857246719

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 #2,635,858

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