Block #530,795

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/8/2014, 2:30:02 AM · Difficulty 10.8930 · 6,272,864 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

141fc8431fa5b10c0045a0fdbf322d0f4f5aab206e579f2c49b0106f28e24e3f

View on Chainz ↗

Height

#530,795

Difficulty

10.892985

Transactions

Size

956 B

Version

Bits

0ae49aad

Nonce

76,434,258

Timestamp

5/8/2014, 2:30:02 AM

Confirmations

6,272,864

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a0449b2ebb0c7eac2a08c3c9ed59518df905bea93b84c5b3d01f1adde11fcbc4

Transactions (3)

Coinbase7079791e3949c0…c62fefcd74f811

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

a730b4af494e20…9fecfd8d6bffd4

3 in → 2 out1723.0504 XPM521 B

AV9McjAn…RKbfWtbx AGStkRb3…Jig8RL33

6369d4e7354bec…778283486857a0

1 in → 2 out2.3010 XPM226 B

AKhgkfA3…aoWaTC9T AcLRkhYZ…uC4J6t43

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.

1.334 × 10¹⁰¹(102-digit number)

13346366013225705821…52774206602853631999

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

1.334 × 10¹⁰¹(102-digit number)

13346366013225705821…52774206602853631999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.334 × 10¹⁰¹(102-digit number)

13346366013225705821…52774206602853632001

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

2.669 × 10¹⁰¹(102-digit number)

26692732026451411642…05548413205707263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.669 × 10¹⁰¹(102-digit number)

26692732026451411642…05548413205707264001

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

5.338 × 10¹⁰¹(102-digit number)

53385464052902823284…11096826411414527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.338 × 10¹⁰¹(102-digit number)

53385464052902823284…11096826411414528001

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

1.067 × 10¹⁰²(103-digit number)

10677092810580564656…22193652822829055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.067 × 10¹⁰²(103-digit number)

10677092810580564656…22193652822829056001

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

2.135 × 10¹⁰²(103-digit number)

21354185621161129313…44387305645658111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.135 × 10¹⁰²(103-digit number)

21354185621161129313…44387305645658112001

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