Block #63,902

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 4:25:32 AM · Difficulty 8.9803 · 6,748,744 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fcb72c638da8f8c1afb097ba54ec9c07f2632b00a42a7e6a0f8d33563e670af5

View on Chainz ↗

Height

#63,902

Difficulty

8.980339

Transactions

Size

724 B

Version

Bits

08faf782

Nonce

Timestamp

7/19/2013, 4:25:32 AM

Confirmations

6,748,744

Mined by

⛏️ P2SHANr46gjzqtEEohkctH9Uj6rSAR39ASbv38

Merkle Root

4cad620dfa24864137fc61117a6a80e1c256382b6b1585497dd75c5170dfff2c

Transactions (2)

Coinbase93aa8efb21ae47…25214053f39f4a

1 in → 1 out12.3900 XPM110 B

ANr46gjz…39ASbv38

95596ab8db5dbd…1fa624cad44d3c

3 in → 2 out46.0929 XPM522 B

AWSS5MMB…C75HTYEC AWsm5dcu…nmgoQtES

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.

1.478 × 10⁹⁸(99-digit number)

14786258718547209069…84971698569987394799

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

1.478 × 10⁹⁸(99-digit number)

14786258718547209069…84971698569987394799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.478 × 10⁹⁸(99-digit number)

14786258718547209069…84971698569987394801

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

2.957 × 10⁹⁸(99-digit number)

29572517437094418139…69943397139974789599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.957 × 10⁹⁸(99-digit number)

29572517437094418139…69943397139974789601

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

5.914 × 10⁹⁸(99-digit number)

59145034874188836278…39886794279949579199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.914 × 10⁹⁸(99-digit number)

59145034874188836278…39886794279949579201

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

1.182 × 10⁹⁹(100-digit number)

11829006974837767255…79773588559899158399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.182 × 10⁹⁹(100-digit number)

11829006974837767255…79773588559899158401

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

2.365 × 10⁹⁹(100-digit number)

23658013949675534511…59547177119798316799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #63,902

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