Block #59,853

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 4:41:23 AM · Difficulty 8.9667 · 6,730,018 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1815f25850f6ce05a45061848e0363499b70c14d94fed2ad1aad4e1ba0fa2e01

View on Chainz ↗

Height

#59,853

Difficulty

8.966729

Transactions

Size

577 B

Version

Bits

08f77b8a

Nonce

937

Timestamp

7/18/2013, 4:41:23 AM

Confirmations

6,730,018

Merkle Root

d7f3c785e3969c2d5a6de0aa3ee67ecd96a3d9743b915b9e72d8c8bdb6ae28fe

Transactions (2)

Coinbase910d180a3d946b…63806aeae6df1b

1 in → 1 out12.4300 XPM110 B

AN6SeE9a…9VNHgDcP

a108f6020ab5d8…645d0c6509d94d

2 in → 2 out272.9700 XPM374 B

AU633Jdy…KKSLpWRp AdbHwMhD…BrWZDcw5

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.

3.930 × 10¹⁰¹(102-digit number)

39308264498229574438…25688612390746035939

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

3.930 × 10¹⁰¹(102-digit number)

39308264498229574438…25688612390746035939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.930 × 10¹⁰¹(102-digit number)

39308264498229574438…25688612390746035941

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

7.861 × 10¹⁰¹(102-digit number)

78616528996459148876…51377224781492071879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.861 × 10¹⁰¹(102-digit number)

78616528996459148876…51377224781492071881

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

1.572 × 10¹⁰²(103-digit number)

15723305799291829775…02754449562984143759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.572 × 10¹⁰²(103-digit number)

15723305799291829775…02754449562984143761

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

3.144 × 10¹⁰²(103-digit number)

31446611598583659550…05508899125968287519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.144 × 10¹⁰²(103-digit number)

31446611598583659550…05508899125968287521

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