Block #935,626

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/14/2015, 5:17:12 AM · Difficulty 10.9009 · 5,870,773 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c579904563637b5137e596cfbad7e3ba13c54622e17dc02771530a80f275a7e

View on Chainz ↗

Height

#935,626

Difficulty

10.900871

Transactions

Size

1.02 KB

Version

Bits

0ae69f80

Nonce

500,238,957

Timestamp

2/14/2015, 5:17:12 AM

Confirmations

5,870,773

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9fc89beb31b59e87c4131fc16080353b72efa49355bd380cb08789d61af713b7

Transactions (5)

Coinbase9fc653c1fdc0e0…3f883d23cc3ede

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

4e93595ca466b6…50047e95eca131

1 in → 1 out8.3900 XPM158 B

AekLq4Sw…ueWMfyir

470f319a2f731a…f02a115a04728c

1 in → 2 out7.7169 XPM225 B

AR1Ck57F…K7ovbM6V AdWEcK3r…HNaeWgVb

36efbe7d74ebc2…a5a0ffa08debde

1 in → 2 out6.5062 XPM225 B

AXrTw46X…e1dGvSFf AUwnqZc1…4RTjG8AT

0ca2ae14f291db…a4eb0adcdc9de8

1 in → 2 out4.9394 XPM226 B

AZCvmw4P…zJBQXgwY Ae7YXEyn…hnSYZsCr

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.

3.674 × 10⁹⁷(98-digit number)

36745491318765670687…09277881318680596479

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

3.674 × 10⁹⁷(98-digit number)

36745491318765670687…09277881318680596479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.674 × 10⁹⁷(98-digit number)

36745491318765670687…09277881318680596481

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

7.349 × 10⁹⁷(98-digit number)

73490982637531341375…18555762637361192959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.349 × 10⁹⁷(98-digit number)

73490982637531341375…18555762637361192961

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

1.469 × 10⁹⁸(99-digit number)

14698196527506268275…37111525274722385919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.469 × 10⁹⁸(99-digit number)

14698196527506268275…37111525274722385921

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

2.939 × 10⁹⁸(99-digit number)

29396393055012536550…74223050549444771839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.939 × 10⁹⁸(99-digit number)

29396393055012536550…74223050549444771841

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

5.879 × 10⁹⁸(99-digit number)

58792786110025073100…48446101098889543679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.879 × 10⁹⁸(99-digit number)

58792786110025073100…48446101098889543681

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

1.175 × 10⁹⁹(100-digit number)

11758557222005014620…96892202197779087359

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 #935,626

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