Block #63,599

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 2:30:59 AM · Difficulty 8.9796 · 6,744,761 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c904797e2177a6328efbc53c8095adc6d3af4202fd33b47aae9f89377367cf97

View on Chainz ↗

Height

#63,599

Difficulty

8.979579

Transactions

Size

725 B

Version

Bits

08fac5a9

Nonce

1,003

Timestamp

7/19/2013, 2:30:59 AM

Confirmations

6,744,761

Mined by

⛏️ P2SHATCaJff9A3xw7b7sWWztP76rpkpPhSdVZj

Merkle Root

b720843ca22c1ba7d297fd76e8868e7adce4c45320a92f950fbc0dd77ad64f9d

Transactions (2)

Coinbasea724f47898aed5…7638f89af6b1ed

1 in → 1 out12.3900 XPM109 B

ATCaJff9…pPhSdVZj

1a1258f0e00384…54bc29b337b98b

3 in → 2 out669.6700 XPM523 B

AHY9WX3s…cbnbZ2hZ AZdThER7…2cMYXweW

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.

9.126 × 10¹⁰²(103-digit number)

91264949204485467477…28925002072648300959

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

9.126 × 10¹⁰²(103-digit number)

91264949204485467477…28925002072648300959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.126 × 10¹⁰²(103-digit number)

91264949204485467477…28925002072648300961

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

1.825 × 10¹⁰³(104-digit number)

18252989840897093495…57850004145296601919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.825 × 10¹⁰³(104-digit number)

18252989840897093495…57850004145296601921

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

3.650 × 10¹⁰³(104-digit number)

36505979681794186990…15700008290593203839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.650 × 10¹⁰³(104-digit number)

36505979681794186990…15700008290593203841

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

7.301 × 10¹⁰³(104-digit number)

73011959363588373981…31400016581186407679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.301 × 10¹⁰³(104-digit number)

73011959363588373981…31400016581186407681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #63,599

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