Block #30,685

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 8:14:53 PM · Difficulty 7.9873 · 6,778,197 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c9590c0cb9c3d98b2cfa003b025f8be09a02e95a8091363bd9cf10a8acc9db4

View on Chainz ↗

Height

#30,685

Difficulty

7.987334

Transactions

Size

359 B

Version

Bits

07fcc1f3

Nonce

362

Timestamp

7/13/2013, 8:14:53 PM

Confirmations

6,778,197

Mined by

⛏️ P2SHAKSwr9eUsXtYAeGKZ6MmF96jvsdLNxuVyn

Merkle Root

b351ce5739dd06eee20e7800983e84c561552c483f202a8967517095edffe24a

Transactions (2)

Coinbasec28ca061cb2c1d…1b86ba6a7a7df9

1 in → 1 out15.6600 XPM108 B

AKSwr9eU…dLNxuVyn

f2c26f945a7cb9…f0b73229c895a9

1 in → 1 out16.0000 XPM157 B

ARyZyeBv…BKDYfhgo

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.

1.084 × 10¹⁰⁵(106-digit number)

10844357307262603786…48564338208245599079

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

1.084 × 10¹⁰⁵(106-digit number)

10844357307262603786…48564338208245599079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.084 × 10¹⁰⁵(106-digit number)

10844357307262603786…48564338208245599081

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

2.168 × 10¹⁰⁵(106-digit number)

21688714614525207572…97128676416491198159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.168 × 10¹⁰⁵(106-digit number)

21688714614525207572…97128676416491198161

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

4.337 × 10¹⁰⁵(106-digit number)

43377429229050415144…94257352832982396319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.337 × 10¹⁰⁵(106-digit number)

43377429229050415144…94257352832982396321

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

8.675 × 10¹⁰⁵(106-digit number)

86754858458100830289…88514705665964792639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 #30,685

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