Block #1,845,678

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/12/2016, 2:12:07 PM · Difficulty 10.6109 · 4,986,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

105c1598857dea0ffb17d273af4b5c3223def04e2b20ebd79a55a7b299915620

View on Chainz ↗

Height

#1,845,678

Difficulty

10.610870

Transactions

Size

2.19 KB

Version

Bits

0a9c61f2

Nonce

299,516,939

Timestamp

11/12/2016, 2:12:07 PM

Confirmations

4,986,046

Mined by

⛏️ P2SHASXaqQQ4CcPGdFaRPV1A9gVZSWtUc6t4zH

Merkle Root

84eb21bace122de2cb738157a1a27358ba5f903dcd08a53a4869a53267e071b9

Transactions (2)

Coinbasea6cbe6858125f7…a041792d2ad443

1 in → 1 out8.9000 XPM109 B

ASXaqQQ4…tUc6t4zH

b9f49eb109e962…07b8cb421cdb37

2 in → 51 out199.6803 XPM1.99 KB

ASDSnPmP…cuZ3dwee AeKC8SAt…RuP19MAr AUQG3FSN…9QJXDotb AGeknUFR…pZpvKHUi AMLrNvv3…jG4bGpcV

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.

1.433 × 10⁹⁴(95-digit number)

14336200427019987078…82339416693443204849

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

1.433 × 10⁹⁴(95-digit number)

14336200427019987078…82339416693443204849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.433 × 10⁹⁴(95-digit number)

14336200427019987078…82339416693443204851

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

2.867 × 10⁹⁴(95-digit number)

28672400854039974156…64678833386886409699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.867 × 10⁹⁴(95-digit number)

28672400854039974156…64678833386886409701

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

5.734 × 10⁹⁴(95-digit number)

57344801708079948313…29357666773772819399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.734 × 10⁹⁴(95-digit number)

57344801708079948313…29357666773772819401

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

1.146 × 10⁹⁵(96-digit number)

11468960341615989662…58715333547545638799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.146 × 10⁹⁵(96-digit number)

11468960341615989662…58715333547545638801

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

2.293 × 10⁹⁵(96-digit number)

22937920683231979325…17430667095091277599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.293 × 10⁹⁵(96-digit number)

22937920683231979325…17430667095091277601

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 #1,845,678

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