Block #422,373

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 4:22:07 PM · Difficulty 10.3803 · 6,386,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99d26a514072e51a30c91d737f3e8e62b80e392e150bb27416b2813d8458e79e

View on Chainz ↗

Height

#422,373

Difficulty

10.380271

Transactions

Size

801 B

Version

Bits

0a615979

Nonce

359,196

Timestamp

2/27/2014, 4:22:07 PM

Confirmations

6,386,058

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9acdc50e542f7346f71011e58fe437e9e2e9f87d5b3f753d13ed2ce48b40b132

Transactions (3)

Coinbase2b777ce48fe3ba…8b4e25ff620bc6

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

e71e4f21ccdf71…6ba536c07f4241

2 in → 2 out30.9823 XPM373 B

AaKi867U…LAMaRHDS ASZkhXuz…nJzSGHeD

4ca468b3416a4f…c25afb0ec1f954

1 in → 2 out6819.7011 XPM226 B

AWwE7aZo…sBga3UPL AXhhDBKe…jAQnsZdV

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.

1.965 × 10¹⁰⁰(101-digit number)

19654971204922133462…57551551409194754479

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

1.965 × 10¹⁰⁰(101-digit number)

19654971204922133462…57551551409194754479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.965 × 10¹⁰⁰(101-digit number)

19654971204922133462…57551551409194754481

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

3.930 × 10¹⁰⁰(101-digit number)

39309942409844266924…15103102818389508959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.930 × 10¹⁰⁰(101-digit number)

39309942409844266924…15103102818389508961

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

7.861 × 10¹⁰⁰(101-digit number)

78619884819688533849…30206205636779017919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.861 × 10¹⁰⁰(101-digit number)

78619884819688533849…30206205636779017921

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

1.572 × 10¹⁰¹(102-digit number)

15723976963937706769…60412411273558035839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.572 × 10¹⁰¹(102-digit number)

15723976963937706769…60412411273558035841

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

3.144 × 10¹⁰¹(102-digit number)

31447953927875413539…20824822547116071679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.144 × 10¹⁰¹(102-digit number)

31447953927875413539…20824822547116071681

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 #422,373

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