Block #355,750

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 8:39:16 AM · Difficulty 10.3638 · 6,440,394 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cddf5e7701cbf73c377f1d70302b600085144cf64f3ab6de7ed711c94e673aca

View on Chainz ↗

Height

#355,750

Difficulty

10.363776

Transactions

Size

3.06 KB

Version

Bits

0a5d206e

Nonce

42,187

Timestamp

1/12/2014, 8:39:16 AM

Confirmations

6,440,394

Mined by

⛏️ maRTAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d3d2bd3082e40e93e96be576fe682a94d40e28fbd26f1468adc636f2bed375b3

Transactions (4)

Coinbase75ba698373d2c6…591899741b764f

1 in → 26 out9.3000 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AZemWJAo…6jhDtieG AXeQnyEs…fUWKQwq8

1722b410acf462…e5f1f5074b9096

1 in → 2 out2498.3934 XPM226 B

Aam1B1Mk…9J8gHLpW AY4H42CP…4bQ4ZA3H

f5470244b6b729…30a632ffbadca7

9 in → 13 out38.4896 XPM1.61 KB

AXvZGQ71…UWV5LuTN Aeuy19AE…uLdad6u2 AbBfJxdv…5LhhDvme ALsbU9Kz…C7sjAXyq AWQhak32…eArVqMxc

d47506c69f8be2…5dec5d7d42f0f0

1 in → 2 out231.4724 XPM226 B

APFB3HGX…FMoE7jFi APywCSHj…o1bJUYmE

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.

1.676 × 10¹⁰³(104-digit number)

16769315301035054396…02799498043382043519

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

1.676 × 10¹⁰³(104-digit number)

16769315301035054396…02799498043382043519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.676 × 10¹⁰³(104-digit number)

16769315301035054396…02799498043382043521

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

3.353 × 10¹⁰³(104-digit number)

33538630602070108793…05598996086764087039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.353 × 10¹⁰³(104-digit number)

33538630602070108793…05598996086764087041

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

6.707 × 10¹⁰³(104-digit number)

67077261204140217587…11197992173528174079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.707 × 10¹⁰³(104-digit number)

67077261204140217587…11197992173528174081

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

1.341 × 10¹⁰⁴(105-digit number)

13415452240828043517…22395984347056348159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.341 × 10¹⁰⁴(105-digit number)

13415452240828043517…22395984347056348161

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

2.683 × 10¹⁰⁴(105-digit number)

26830904481656087034…44791968694112696319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.683 × 10¹⁰⁴(105-digit number)

26830904481656087034…44791968694112696321

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