Block #46,746

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 7:44:23 AM · Difficulty 8.8016 · 6,743,291 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

437815cb6346eef669039909b73d39815e87c52830d58988f16e57573f95832f

View on Chainz ↗

Height

#46,746

Difficulty

8.801627

Transactions

Size

6.84 KB

Version

Bits

08cd3775

Nonce

289

Timestamp

7/15/2013, 7:44:23 AM

Confirmations

6,743,291

Merkle Root

549a78a4959491d7b39f402cdfc3ac884fd3fe3cb68501836b1c1c90e8cd58e4

Transactions (2)

Coinbase01895eb856d492…ec4584842e72a0

1 in → 1 out12.9600 XPM110 B

ANCYL9xh…9WyGnqDE

8ada7dde3b28a9…c6562eca6fb692

59 in → 1 out800.0000 XPM6.65 KB

AduwKP5J…wp1LyLxL

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.

1.990 × 10⁸⁷(88-digit number)

19905059095573976122…17051406782631525049

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

1.990 × 10⁸⁷(88-digit number)

19905059095573976122…17051406782631525049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.990 × 10⁸⁷(88-digit number)

19905059095573976122…17051406782631525051

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

3.981 × 10⁸⁷(88-digit number)

39810118191147952245…34102813565263050099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.981 × 10⁸⁷(88-digit number)

39810118191147952245…34102813565263050101

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

7.962 × 10⁸⁷(88-digit number)

79620236382295904491…68205627130526100199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.962 × 10⁸⁷(88-digit number)

79620236382295904491…68205627130526100201

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

1.592 × 10⁸⁸(89-digit number)

15924047276459180898…36411254261052200399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.592 × 10⁸⁸(89-digit number)

15924047276459180898…36411254261052200401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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