Block #858,603

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2014, 6:22:36 PM · Difficulty 10.9665 · 5,968,533 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96034f7b0f9476c1ad73758c3659cb7ee15fe302e547cfa8e26ba38b459a5a15

View on Chainz ↗

Height

#858,603

Difficulty

10.966521

Transactions

Size

979 B

Version

Bits

0af76de4

Nonce

322,996,171

Timestamp

12/18/2014, 6:22:36 PM

Confirmations

5,968,533

Mined by

⛏️ P2SHAHbMsPBvLSf1UrX5anAiYvNP4oL24bgDKA

Merkle Root

b0f5fb4302fa948311df9268f85ce7702fef36311c04f69eafb5134f8709c1b1

Transactions (4)

Coinbasec885e9c1a5cf19…0853d6249459d4

1 in → 1 out8.3450 XPM109 B

AHbMsPBv…L24bgDKA

3f2601e86be2fd…700d585fc9e6e6

1 in → 3 out0.5472 XPM261 B

AWXQpZ9S…xNAMoHLk AQk78hHj…pKfZ6aWw AYCrJ6bE…jvvxQ5Qs

1885b8de47bf48…ccbf4776ed4785

1 in → 3 out0.3862 XPM259 B

AMZoL8oM…dwymvZLf AXJLhntR…bgw7mUJr APodd6Ty…SkcaYVRG

4c92e0894e82a5…21ba65ad1fc0af

1 in → 3 out0.3862 XPM260 B

AKkb36DL…KRif6vNW AM23WRGo…wMnMRgwG AZpWSv1M…pVu5Efm4

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.

6.432 × 10⁹⁵(96-digit number)

64322118394278189699…51335244407062051839

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

6.432 × 10⁹⁵(96-digit number)

64322118394278189699…51335244407062051839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.432 × 10⁹⁵(96-digit number)

64322118394278189699…51335244407062051841

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

1.286 × 10⁹⁶(97-digit number)

12864423678855637939…02670488814124103679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.286 × 10⁹⁶(97-digit number)

12864423678855637939…02670488814124103681

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

2.572 × 10⁹⁶(97-digit number)

25728847357711275879…05340977628248207359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.572 × 10⁹⁶(97-digit number)

25728847357711275879…05340977628248207361

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

5.145 × 10⁹⁶(97-digit number)

51457694715422551759…10681955256496414719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.145 × 10⁹⁶(97-digit number)

51457694715422551759…10681955256496414721

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

1.029 × 10⁹⁷(98-digit number)

10291538943084510351…21363910512992829439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.029 × 10⁹⁷(98-digit number)

10291538943084510351…21363910512992829441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #858,603

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