Block #94,486

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/3/2013, 3:16:20 AM · Difficulty 9.2028 · 6,715,930 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

839fd897aea710f888097a9cd662d55b46709d1e2bcbdf7501d016204e9e9ec7

View on Chainz ↗

Height

#94,486

Difficulty

9.202841

Transactions

Size

851 B

Version

Bits

0933ed63

Nonce

11,527

Timestamp

8/3/2013, 3:16:20 AM

Confirmations

6,715,930

Mined by

⛏️ P2SHAJRResfErLFjYy7JkL43nMZLDLzxVaUkfq

Merkle Root

0a91b16f6b90b93556f7b5a8fa4991c91e24e1b19ab6ae331bbe921d61b0b99e

Transactions (3)

Coinbase2fc15f90661744…56ab7651d0fca0

1 in → 1 out11.8100 XPM109 B

AJRResfE…zxVaUkfq

7c8864b3142d69…df34483bdc5ab2

2 in → 1 out23.3600 XPM272 B

AUyL3rcf…PuULqq4T

2a5f8743585fd6…86e0416c3f4734

2 in → 2 out18.2718 XPM374 B

AHvHoiFk…DPo5SxsB AeDG2eMq…VZum6qqh

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.

4.566 × 10¹⁰⁸(109-digit number)

45661791674971374929…54584633713490765899

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

4.566 × 10¹⁰⁸(109-digit number)

45661791674971374929…54584633713490765899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.566 × 10¹⁰⁸(109-digit number)

45661791674971374929…54584633713490765901

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

9.132 × 10¹⁰⁸(109-digit number)

91323583349942749859…09169267426981531799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.132 × 10¹⁰⁸(109-digit number)

91323583349942749859…09169267426981531801

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

1.826 × 10¹⁰⁹(110-digit number)

18264716669988549971…18338534853963063599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.826 × 10¹⁰⁹(110-digit number)

18264716669988549971…18338534853963063601

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

3.652 × 10¹⁰⁹(110-digit number)

36529433339977099943…36677069707926127199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.652 × 10¹⁰⁹(110-digit number)

36529433339977099943…36677069707926127201

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

7.305 × 10¹⁰⁹(110-digit number)

73058866679954199887…73354139415852254399

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 #94,486

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