Block #402,786

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 4:41:07 PM · Difficulty 10.4360 · 6,407,589 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50757a7cc05f7f44215c5bcc8ac83aeab1e338628cb8515f053e6e5a1cb493c6

View on Chainz ↗

Height

#402,786

Difficulty

10.436040

Transactions

Size

586 B

Version

Bits

0a6fa051

Nonce

4,036

Timestamp

2/13/2014, 4:41:07 PM

Confirmations

6,407,589

Mined by

⛏️ P2SHALRPVUxqedLrrEoUesNYYkDLJ6f1KpPKUq

Merkle Root

db7f47ebbdaa167d41ff4e934e9af034bc26192c1c90255314b88761022bc652

Transactions (3)

Coinbase9ad6a364c169d7…91a6cb25d3a08e

1 in → 1 out9.1900 XPM109 B

ALRPVUxq…f1KpPKUq

368acd1b3b2382…4b63ecd4d9abc0

1 in → 1 out3.0027 XPM192 B

AWvjJGfi…LAHUcBRf

752ea0d3803551…45f3db29ea4ae1

1 in → 1 out3.0803 XPM193 B

AUxEcm33…ZQTLzUND

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.

1.409 × 10¹⁰⁰(101-digit number)

14095307571980917655…30171543190411585559

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

1.409 × 10¹⁰⁰(101-digit number)

14095307571980917655…30171543190411585559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.409 × 10¹⁰⁰(101-digit number)

14095307571980917655…30171543190411585561

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

2.819 × 10¹⁰⁰(101-digit number)

28190615143961835311…60343086380823171119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.819 × 10¹⁰⁰(101-digit number)

28190615143961835311…60343086380823171121

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

5.638 × 10¹⁰⁰(101-digit number)

56381230287923670622…20686172761646342239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.638 × 10¹⁰⁰(101-digit number)

56381230287923670622…20686172761646342241

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

1.127 × 10¹⁰¹(102-digit number)

11276246057584734124…41372345523292684479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.127 × 10¹⁰¹(102-digit number)

11276246057584734124…41372345523292684481

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

2.255 × 10¹⁰¹(102-digit number)

22552492115169468249…82744691046585368959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.255 × 10¹⁰¹(102-digit number)

22552492115169468249…82744691046585368961

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 #402,786

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