Block #522,769

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2014, 5:45:12 AM · Difficulty 10.8685 · 6,281,142 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8d5b5dd2b913c8d8048b1d611df04811f4773dcc1ff9d93a0403361015f9d9b0

View on Chainz ↗

Height

#522,769

Difficulty

10.868450

Transactions

Size

796 B

Version

Bits

0ade52bf

Nonce

55,045,055

Timestamp

5/3/2014, 5:45:12 AM

Confirmations

6,281,142

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

38acd3ccd36f69b4fd984954a2a33a72314d94ced562421553ecbeeaf54edc59

Transactions (2)

Coinbase55fbf38838700e…fe5747a8270b80

1 in → 1 out8.4600 XPM116 B

AbwWkWZt…kawDhufa

9eb8f331335d8c…e9b47bea3ba8c9

3 in → 5 out12.3534 XPM588 B

AeKNrjNj…1NEq95Ta ALahtnF9…EBJmNW8D AGRJf5c9…j28JnLsV AXbbkuVv…UixHY7hn AHbu8w6V…13P7BwSQ

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.

6.105 × 10⁹⁹(100-digit number)

61052882130981122059…29602115377920844799

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

6.105 × 10⁹⁹(100-digit number)

61052882130981122059…29602115377920844799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.105 × 10⁹⁹(100-digit number)

61052882130981122059…29602115377920844801

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

1.221 × 10¹⁰⁰(101-digit number)

12210576426196224411…59204230755841689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.221 × 10¹⁰⁰(101-digit number)

12210576426196224411…59204230755841689601

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

2.442 × 10¹⁰⁰(101-digit number)

24421152852392448823…18408461511683379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.442 × 10¹⁰⁰(101-digit number)

24421152852392448823…18408461511683379201

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

4.884 × 10¹⁰⁰(101-digit number)

48842305704784897647…36816923023366758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.884 × 10¹⁰⁰(101-digit number)

48842305704784897647…36816923023366758401

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

9.768 × 10¹⁰⁰(101-digit number)

97684611409569795294…73633846046733516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.768 × 10¹⁰⁰(101-digit number)

97684611409569795294…73633846046733516801

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