Block #101,486

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/6/2013, 4:12:31 PM · Difficulty 9.4631 · 6,715,210 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8dcf702ee6e6ba45cc2e5b81e6343703d39be2782e04e3c014ab1ae5f224c30b

View on Chainz ↗

Height

#101,486

Difficulty

9.463071

Transactions

Size

584 B

Version

Bits

09768bce

Nonce

4,953

Timestamp

8/6/2013, 4:12:31 PM

Confirmations

6,715,210

Mined by

⛏️ P2SHANuNqCATay2aXyYLSXcE277jKnRP5qnpaL

Merkle Root

eba648103faa8a81a67d3c3a5e329f09c154807313a4259b273bf4ae8c26d459

Transactions (3)

Coinbasead501d0cec958d…4bd9a63ab9a370

1 in → 1 out11.1700 XPM109 B

ANuNqCAT…RP5qnpaL

ce822c02564716…e101ce3af367f2

1 in → 1 out11.4800 XPM158 B

Ad91bTac…3L6H7xaC

27948c0f569f6f…7257c02157b50a

1 in → 2 out4.3176 XPM226 B

ANwBprjn…akrrQSnP ASeroE8U…9NS9as8W

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.

1.072 × 10⁹⁷(98-digit number)

10725379482945811412…40858275777029666839

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

1.072 × 10⁹⁷(98-digit number)

10725379482945811412…40858275777029666839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.072 × 10⁹⁷(98-digit number)

10725379482945811412…40858275777029666841

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

2.145 × 10⁹⁷(98-digit number)

21450758965891622824…81716551554059333679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.145 × 10⁹⁷(98-digit number)

21450758965891622824…81716551554059333681

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

4.290 × 10⁹⁷(98-digit number)

42901517931783245649…63433103108118667359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.290 × 10⁹⁷(98-digit number)

42901517931783245649…63433103108118667361

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

8.580 × 10⁹⁷(98-digit number)

85803035863566491298…26866206216237334719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.580 × 10⁹⁷(98-digit number)

85803035863566491298…26866206216237334721

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

1.716 × 10⁹⁸(99-digit number)

17160607172713298259…53732412432474669439

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 #101,486

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