Block #858,503

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/18/2014, 4:19:20 PM · Difficulty 10.9667 · 5,986,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8afdcd80433a638e23fc8e71278e6574c3430e18c2ae70d190ea92a2dc6abc94

View on Chainz ↗

Height

#858,503

Difficulty

10.966676

Transactions

Size

1.08 KB

Version

Bits

0af77813

Nonce

1,246,265,331

Timestamp

12/18/2014, 4:19:20 PM

Confirmations

5,986,426

Mined by

⛏️ P2SHAULY2pjcxaZL8LG72BvVyaaH2AephkB2qi

Merkle Root

16f4718099eedd7ea99f85c1a5f7100694610968a8be20d9504c65cbc190e3e3

Transactions (5)

Coinbasea7409e78f26bdf…f250baee3df4ec

1 in → 1 out8.3600 XPM109 B

AULY2pjc…ephkB2qi

cf05e3e3535746…8a40330a2027e9

1 in → 2 out0.0901 XPM226 B

AdQHELy7…V9BsPp1k AKQkEo8D…1er6SxPt

8056dbd79f767a…de83e8b7c944d7

1 in → 2 out0.1031 XPM225 B

AMddbcvA…rD5vH1JF AWMk2GLy…w9mmGtPJ

09d8db9b611dee…eea10fc35cdb04

1 in → 2 out0.0643 XPM225 B

AMUThd9C…dQrmAozk AbgCRgZb…wM1ZMLi8

fb21713f2020f0…00cf7d9ea2e9eb

1 in → 2 out0.1031 XPM226 B

AMnGojAT…WwGcvA6U ANNFfF2Y…gJG5yAHL

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.

2.543 × 10⁹³(94-digit number)

25433433159517566205…13466057579344705519

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

2.543 × 10⁹³(94-digit number)

25433433159517566205…13466057579344705519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.543 × 10⁹³(94-digit number)

25433433159517566205…13466057579344705521

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

5.086 × 10⁹³(94-digit number)

50866866319035132411…26932115158689411039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.086 × 10⁹³(94-digit number)

50866866319035132411…26932115158689411041

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

1.017 × 10⁹⁴(95-digit number)

10173373263807026482…53864230317378822079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.017 × 10⁹⁴(95-digit number)

10173373263807026482…53864230317378822081

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

2.034 × 10⁹⁴(95-digit number)

20346746527614052964…07728460634757644159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.034 × 10⁹⁴(95-digit number)

20346746527614052964…07728460634757644161

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

4.069 × 10⁹⁴(95-digit number)

40693493055228105929…15456921269515288319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.069 × 10⁹⁴(95-digit number)

40693493055228105929…15456921269515288321

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.138 × 10⁹⁴(95-digit number)

81386986110456211858…30913842539030576639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #858,503

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