Block #104,285

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/7/2013, 11:40:55 PM · Difficulty 9.5528 · 6,704,204 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01d04bb0a6d8416dcc2afce8b12a15d64380c5cc29189c0027991063cdf31d13

View on Chainz ↗

Height

#104,285

Difficulty

9.552796

Transactions

Size

6.01 KB

Version

Bits

098d840e

Nonce

471,288

Timestamp

8/7/2013, 11:40:55 PM

Confirmations

6,704,204

Mined by

⛏️ P2SHARz2PVbkSaDQss5URRhu5rHY845Tdbma1y

Merkle Root

b158b13469a9e7ac080fce2f337c53d3759b8cd27f051c770e333354cf3e9a24

Transactions (3)

Coinbase6d5527c59100e5…0340380e50faab

1 in → 1 out11.0100 XPM109 B

ARz2PVbk…5Tdbma1y

86174508bd7270…43a56a903369e6

46 in → 1 out516.5900 XPM5.16 KB

AdNeXXkk…QpfXAns4

2160c75db33963…bea3ce851baf46

4 in → 2 out16.0627 XPM670 B

Af53UMZy…ZiWFfNj3 ASk1rWBV…kXD4Ftjn

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.

3.196 × 10⁹⁵(96-digit number)

31967492199316427077…46977187560903443959

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

3.196 × 10⁹⁵(96-digit number)

31967492199316427077…46977187560903443959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.196 × 10⁹⁵(96-digit number)

31967492199316427077…46977187560903443961

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

6.393 × 10⁹⁵(96-digit number)

63934984398632854154…93954375121806887919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.393 × 10⁹⁵(96-digit number)

63934984398632854154…93954375121806887921

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

1.278 × 10⁹⁶(97-digit number)

12786996879726570830…87908750243613775839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.278 × 10⁹⁶(97-digit number)

12786996879726570830…87908750243613775841

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

2.557 × 10⁹⁶(97-digit number)

25573993759453141661…75817500487227551679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.557 × 10⁹⁶(97-digit number)

25573993759453141661…75817500487227551681

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

5.114 × 10⁹⁶(97-digit number)

51147987518906283323…51635000974455103359

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 #104,285

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