Block #453,879

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 2:01:53 PM · Difficulty 10.3929 · 6,360,421 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

20193dd41c7593c1bfe0b2e79bf74e556239e3e2aa5a6261babcf1e00dbb132c

View on Chainz ↗

Height

#453,879

Difficulty

10.392897

Transactions

Size

834 B

Version

Bits

0a6494e1

Nonce

16,799

Timestamp

3/21/2014, 2:01:53 PM

Confirmations

6,360,421

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

bbde7a770470362c4e1f5d2f39150088381b834b51e274458e3c4559126555fd

Transactions (1)

Coinbasebbde7a77047036…3c4559126555fd

1 in → 20 out9.2400 XPM743 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AbHY4iza…Yckt2J5W AbPcCMg4…719q6mAX

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.

6.822 × 10⁹⁷(98-digit number)

68229502888835015319…76289443348253985519

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

6.822 × 10⁹⁷(98-digit number)

68229502888835015319…76289443348253985519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.822 × 10⁹⁷(98-digit number)

68229502888835015319…76289443348253985521

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

1.364 × 10⁹⁸(99-digit number)

13645900577767003063…52578886696507971039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.364 × 10⁹⁸(99-digit number)

13645900577767003063…52578886696507971041

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

2.729 × 10⁹⁸(99-digit number)

27291801155534006127…05157773393015942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.729 × 10⁹⁸(99-digit number)

27291801155534006127…05157773393015942081

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

5.458 × 10⁹⁸(99-digit number)

54583602311068012255…10315546786031884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.458 × 10⁹⁸(99-digit number)

54583602311068012255…10315546786031884161

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

1.091 × 10⁹⁹(100-digit number)

10916720462213602451…20631093572063768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.091 × 10⁹⁹(100-digit number)

10916720462213602451…20631093572063768321

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 #453,879

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