Block #622,608

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/8/2014, 2:04:24 AM · Difficulty 10.9545 · 6,182,792 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

11f02cec5e8a4ce1c2fc5ce644e178885f7444a46a1fcfeae295d23942c40a70

View on Chainz ↗

Height

#622,608

Difficulty

10.954514

Transactions

Size

549 B

Version

Bits

0af45b0f

Nonce

1,618,306

Timestamp

7/8/2014, 2:04:24 AM

Confirmations

6,182,792

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f20457fbdd4baf4998e2461bed076b35a822fa60a8b1b7a831c05eb8b8063553

Transactions (2)

Coinbase8a6a526fe1ce43…fe0e7ea4300baa

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

2366e837489ac3…179662793a2650

2 in → 1 out64.7700 XPM341 B

APNmZ1c8…oBrRj6mg

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.

3.029 × 10¹⁰⁰(101-digit number)

30298461970372041140…07751842006975938559

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

3.029 × 10¹⁰⁰(101-digit number)

30298461970372041140…07751842006975938559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.029 × 10¹⁰⁰(101-digit number)

30298461970372041140…07751842006975938561

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

6.059 × 10¹⁰⁰(101-digit number)

60596923940744082280…15503684013951877119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.059 × 10¹⁰⁰(101-digit number)

60596923940744082280…15503684013951877121

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

1.211 × 10¹⁰¹(102-digit number)

12119384788148816456…31007368027903754239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.211 × 10¹⁰¹(102-digit number)

12119384788148816456…31007368027903754241

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

2.423 × 10¹⁰¹(102-digit number)

24238769576297632912…62014736055807508479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.423 × 10¹⁰¹(102-digit number)

24238769576297632912…62014736055807508481

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

4.847 × 10¹⁰¹(102-digit number)

48477539152595265824…24029472111615016959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.847 × 10¹⁰¹(102-digit number)

48477539152595265824…24029472111615016961

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