Block #85,641

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 1:53:20 PM · Difficulty 9.2916 · 6,730,794 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2613b04e93fa709cc4b9ffc66c18b2e458e2b29b422e2a0aaed02bbdaa671c27

View on Chainz ↗

Height

#85,641

Difficulty

9.291597

Transactions

Size

946 B

Version

Bits

094aa612

Nonce

266,133

Timestamp

7/27/2013, 1:53:20 PM

Confirmations

6,730,794

Mined by

⛏️ P2SHAJ2ycoYevQyQ38KDRWF1e4Le3WT4f7wgF6

Merkle Root

7538d2a3a23f7ffaa89dc9eccea824c206023a2febffa802e5cb2f0acf34e864

Transactions (3)

Coinbaseb81eafcd12384f…109a461c65540e

1 in → 1 out11.5900 XPM109 B

AJ2ycoYe…T4f7wgF6

39c12f0a5b4ff8…625406f58bf1a8

3 in → 2 out60.6959 XPM520 B

Aa9DBGts…dmsea2S5 AXXD9rC2…Vb5reFe7

2134746a12a6fc…40740fbcafdb47

1 in → 2 out27.0474 XPM225 B

AK1ZVFqJ…KGar1LEW AFnatN4B…qzfTV94h

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.

1.905 × 10⁹⁹(100-digit number)

19050537533722615307…81002558878982001669

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

1.905 × 10⁹⁹(100-digit number)

19050537533722615307…81002558878982001669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.905 × 10⁹⁹(100-digit number)

19050537533722615307…81002558878982001671

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

3.810 × 10⁹⁹(100-digit number)

38101075067445230614…62005117757964003339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.810 × 10⁹⁹(100-digit number)

38101075067445230614…62005117757964003341

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

7.620 × 10⁹⁹(100-digit number)

76202150134890461228…24010235515928006679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.620 × 10⁹⁹(100-digit number)

76202150134890461228…24010235515928006681

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

1.524 × 10¹⁰⁰(101-digit number)

15240430026978092245…48020471031856013359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.524 × 10¹⁰⁰(101-digit number)

15240430026978092245…48020471031856013361

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

3.048 × 10¹⁰⁰(101-digit number)

30480860053956184491…96040942063712026719

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 #85,641

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