Block #427,336

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 7:38:15 AM · Difficulty 10.3478 · 6,378,474 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23d1494aacd645b2a1513f365f4f00e8843fd4da5cba419b8cc76c857103bd62

View on Chainz ↗

Height

#427,336

Difficulty

10.347767

Transactions

Size

913 B

Version

Bits

0a59073a

Nonce

72,993

Timestamp

3/3/2014, 7:38:15 AM

Confirmations

6,378,474

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7c59904ade01146fdb00dd5f1d8348dfd3a4db949d74f05426d5e398a8bbd362

Transactions (4)

Coinbasefc4fdbecf7b181…ff36b846ed572d

1 in → 1 out9.3500 XPM110 B

AeKNrjNj…1NEq95Ta

1a4200bbf9b06b…9af646b525fe19

1 in → 2 out7.1784 XPM226 B

ARqf6Rwd…1pxF55hf AQs1rTbm…aZ35eg3w

e51ab3ecea04f6…139d46af7b9fd0

1 in → 2 out5.1537 XPM226 B

APyCJcr1…QAhukZCb AXZXx8Ut…kiHrXp7X

01306598c3bd9f…4b5b82f160f0a4

1 in → 3 out9.5377 XPM259 B

AGKsGytR…WW4z5VzK AUoAjuAg…oYcX3CJZ AZ3JQyet…geMSTshf

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.

2.040 × 10¹⁰⁰(101-digit number)

20403207124284110083…15823553674721718059

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

2.040 × 10¹⁰⁰(101-digit number)

20403207124284110083…15823553674721718059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.040 × 10¹⁰⁰(101-digit number)

20403207124284110083…15823553674721718061

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

4.080 × 10¹⁰⁰(101-digit number)

40806414248568220166…31647107349443436119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.080 × 10¹⁰⁰(101-digit number)

40806414248568220166…31647107349443436121

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

8.161 × 10¹⁰⁰(101-digit number)

81612828497136440333…63294214698886872239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.161 × 10¹⁰⁰(101-digit number)

81612828497136440333…63294214698886872241

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

1.632 × 10¹⁰¹(102-digit number)

16322565699427288066…26588429397773744479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.632 × 10¹⁰¹(102-digit number)

16322565699427288066…26588429397773744481

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

3.264 × 10¹⁰¹(102-digit number)

32645131398854576133…53176858795547488959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.264 × 10¹⁰¹(102-digit number)

32645131398854576133…53176858795547488961

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