Block #375,327

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 3:36:17 PM · Difficulty 10.4233 · 6,419,473 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e275ae9d238158290f14adf61f7a736e8dbeedd1200513188f456bb76ca7a154

View on Chainz ↗

Height

#375,327

Difficulty

10.423256

Transactions

Size

2.46 KB

Version

Bits

0a6c5a7c

Nonce

16,165

Timestamp

1/25/2014, 3:36:17 PM

Confirmations

6,419,473

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

03eca8fe6d88187d575b2ae0e6b6a7975b13cb74bda9910da8bf6d9bd9c72600

Transactions (4)

Coinbase8183b5ce849d0e…87e09cda50a41a

1 in → 20 out9.1900 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

2413be31a95fff…e474802ada9cb4

2 in → 2 out3.8066 XPM374 B

AaRXVyQP…gsQ6pvBk AHA7dZy1…7oK4wwr6

3238aa5c14047d…d9792fecf21bf5

5 in → 14 out41.4449 XPM1.06 KB

AXHE8UxM…QrN9C5Yz AGc5kjgR…3FNBfh6y AQPsd5v9…3JF1R7EY AXwECA7B…7uyqxkcd AJyGidYK…wD9VP2WE

1d37c735c0050d…94746fd1c1f01a

1 in → 2 out7812.7174 XPM226 B

ARX2Z3qJ…Jw6xSCjC ATnQqGjC…ESMQczrk

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.

2.698 × 10⁹⁹(100-digit number)

26982308011393393052…79128838911698287999

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

2.698 × 10⁹⁹(100-digit number)

26982308011393393052…79128838911698287999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.698 × 10⁹⁹(100-digit number)

26982308011393393052…79128838911698288001

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

5.396 × 10⁹⁹(100-digit number)

53964616022786786104…58257677823396575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.396 × 10⁹⁹(100-digit number)

53964616022786786104…58257677823396576001

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

1.079 × 10¹⁰⁰(101-digit number)

10792923204557357220…16515355646793151999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.079 × 10¹⁰⁰(101-digit number)

10792923204557357220…16515355646793152001

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

2.158 × 10¹⁰⁰(101-digit number)

21585846409114714441…33030711293586303999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.158 × 10¹⁰⁰(101-digit number)

21585846409114714441…33030711293586304001

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

4.317 × 10¹⁰⁰(101-digit number)

43171692818229428883…66061422587172607999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.317 × 10¹⁰⁰(101-digit number)

43171692818229428883…66061422587172608001

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