Block #470,622

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 1:12:33 AM · Difficulty 10.4302 · 6,328,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cab5ed93a74e10d5938b3d9e3e898024a0b82f9c028f3bd52654b8c8db20e27b

View on Chainz ↗

Height

#470,622

Difficulty

10.430217

Transactions

Size

1.01 KB

Version

Bits

0a6e22ac

Nonce

257,475

Timestamp

4/2/2014, 1:12:33 AM

Confirmations

6,328,058

Mined by

⛏️ ^.aS;cYAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

29f8a71cf8e0e0deca1c47a0565a7c84fe807c1a1da3885dffae7ac5af086f3d

Transactions (1)

Coinbase29f8a71cf8e0e0…ae7ac5af086f3d

1 in → 26 out9.1800 XPM947 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 AebWhrRm…K61Qrkws

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.

4.613 × 10⁹⁸(99-digit number)

46132659334296291517…31637951308843498399

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

4.613 × 10⁹⁸(99-digit number)

46132659334296291517…31637951308843498399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.613 × 10⁹⁸(99-digit number)

46132659334296291517…31637951308843498401

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

9.226 × 10⁹⁸(99-digit number)

92265318668592583035…63275902617686996799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.226 × 10⁹⁸(99-digit number)

92265318668592583035…63275902617686996801

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

1.845 × 10⁹⁹(100-digit number)

18453063733718516607…26551805235373993599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.845 × 10⁹⁹(100-digit number)

18453063733718516607…26551805235373993601

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

3.690 × 10⁹⁹(100-digit number)

36906127467437033214…53103610470747987199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.690 × 10⁹⁹(100-digit number)

36906127467437033214…53103610470747987201

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

7.381 × 10⁹⁹(100-digit number)

73812254934874066428…06207220941495974399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.381 × 10⁹⁹(100-digit number)

73812254934874066428…06207220941495974401

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