Block #636,530

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/17/2014, 12:03:07 AM · Difficulty 10.9637 · 6,188,297 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

177680341fbeec874ef24a7739e16fd59c6a0ece5ab46a1a58624fdf02342e07

View on Chainz ↗

Height

#636,530

Difficulty

10.963720

Transactions

Size

885 B

Version

Bits

0af6b65c

Nonce

1,980,562,100

Timestamp

7/17/2014, 12:03:07 AM

Confirmations

6,188,297

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fa4fa513c4df19aed76796f450ec57db2e4edca5de5f539421b59999b1fcc864

Transactions (4)

Coinbasead731fb2b592c2…f3ee81b6b3e8d6

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

55ea2da06e76ab…357dddcec9341e

1 in → 2 out6.1890 XPM227 B

AeDeccoS…PoFHQLnJ ANZkGcZd…aMusM8ro

77f6057c27f196…3aeb7c976adc26

1 in → 2 out2.2434 XPM226 B

Aa6m331p…NVBR9cYG AUL99Tiv…m1V3MtCa

68c8d5fd646918…e8695204b0966c

1 in → 2 out1.1478 XPM226 B

AM4wMQem…CWfNQVCW AZ6Gz4Hj…SSZgSkm3

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.

7.948 × 10⁹⁵(96-digit number)

79486900744118861481…78751118375094629439

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

7.948 × 10⁹⁵(96-digit number)

79486900744118861481…78751118375094629439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.948 × 10⁹⁵(96-digit number)

79486900744118861481…78751118375094629441

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

1.589 × 10⁹⁶(97-digit number)

15897380148823772296…57502236750189258879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.589 × 10⁹⁶(97-digit number)

15897380148823772296…57502236750189258881

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

3.179 × 10⁹⁶(97-digit number)

31794760297647544592…15004473500378517759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.179 × 10⁹⁶(97-digit number)

31794760297647544592…15004473500378517761

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

6.358 × 10⁹⁶(97-digit number)

63589520595295089185…30008947000757035519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.358 × 10⁹⁶(97-digit number)

63589520595295089185…30008947000757035521

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

1.271 × 10⁹⁷(98-digit number)

12717904119059017837…60017894001514071039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.271 × 10⁹⁷(98-digit number)

12717904119059017837…60017894001514071041

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 #636,530

Cookie Preferences