Block #430,594

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 2:31:55 PM · Difficulty 10.3456 · 6,373,163 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0463f6727d3e3d53db0f1b77ed11bc424448db2407d65cddf38e0695f0ba5df9

View on Chainz ↗

Height

#430,594

Difficulty

10.345627

Transactions

Size

1003 B

Version

Bits

0a587afd

Nonce

182,128

Timestamp

3/5/2014, 2:31:55 PM

Confirmations

6,373,163

Mined by

⛏️ aS5AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e6fbc4d2a1111e9d3e37dc64c72fd433d038d83b646a422cbc642debe69fdc90

Transactions (1)

Coinbasee6fbc4d2a1111e…642debe69fdc90

1 in → 25 out9.3300 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AJLB8H7s…MRD4s5wA AGKhfQo2…h7fBXLX6

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.

5.910 × 10⁹⁵(96-digit number)

59106243772620288832…18756009855259596799

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

5.910 × 10⁹⁵(96-digit number)

59106243772620288832…18756009855259596799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.910 × 10⁹⁵(96-digit number)

59106243772620288832…18756009855259596801

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

1.182 × 10⁹⁶(97-digit number)

11821248754524057766…37512019710519193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.182 × 10⁹⁶(97-digit number)

11821248754524057766…37512019710519193601

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

2.364 × 10⁹⁶(97-digit number)

23642497509048115533…75024039421038387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.364 × 10⁹⁶(97-digit number)

23642497509048115533…75024039421038387201

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

4.728 × 10⁹⁶(97-digit number)

47284995018096231066…50048078842076774399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.728 × 10⁹⁶(97-digit number)

47284995018096231066…50048078842076774401

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

9.456 × 10⁹⁶(97-digit number)

94569990036192462132…00096157684153548799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.456 × 10⁹⁶(97-digit number)

94569990036192462132…00096157684153548801

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