Block #600,058

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/24/2014, 3:04:51 AM · Difficulty 10.9252 · 6,195,628 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

112522fc18a8e2916422e95c7302a57ef82a544ab9dcc74ef1697f20e13f412e

View on Chainz ↗

Height

#600,058

Difficulty

10.925152

Transactions

Size

615 B

Version

Bits

0aecd6c9

Nonce

93,203,976

Timestamp

6/24/2014, 3:04:51 AM

Confirmations

6,195,628

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cfbf3c70ee5a9a66fb45ef5c1bd4976ef3e8ddbf7704c47083b6a05e637b9125

Transactions (2)

Coinbasec6d79b8bd112c1…d40167f5b8299b

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

e71d269f23f7f2…593afeaf989c36

2 in → 4 out9.2238 XPM408 B

AeKNrjNj…1NEq95Ta ATXFZVYv…JduPzKNb AHXJ1dhk…mhL46N6m AGqSWjWQ…gzSSkRFQ

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.

1.761 × 10⁹⁸(99-digit number)

17615437836706998781…35407831034880312639

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

1.761 × 10⁹⁸(99-digit number)

17615437836706998781…35407831034880312639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.761 × 10⁹⁸(99-digit number)

17615437836706998781…35407831034880312641

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

3.523 × 10⁹⁸(99-digit number)

35230875673413997562…70815662069760625279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.523 × 10⁹⁸(99-digit number)

35230875673413997562…70815662069760625281

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

7.046 × 10⁹⁸(99-digit number)

70461751346827995125…41631324139521250559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.046 × 10⁹⁸(99-digit number)

70461751346827995125…41631324139521250561

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

1.409 × 10⁹⁹(100-digit number)

14092350269365599025…83262648279042501119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.409 × 10⁹⁹(100-digit number)

14092350269365599025…83262648279042501121

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

2.818 × 10⁹⁹(100-digit number)

28184700538731198050…66525296558085002239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.818 × 10⁹⁹(100-digit number)

28184700538731198050…66525296558085002241

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