Block #11,032

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 5:14:25 AM · Difficulty 7.7004 · 6,780,678 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ddabd9cb7fd125e82bc26c4156d392a716fda1744421a4f2a31da84d8f4b40ef

View on Chainz ↗

Height

#11,032

Difficulty

7.700412

Transactions

Size

389 B

Version

Bits

07b34e33

Nonce

Timestamp

7/11/2013, 5:14:25 AM

Confirmations

6,780,678

Merkle Root

1369da2b023a988f3a5282c659e993db0d84a4b7584cb081eb9a10864c38736d

Transactions (2)

Coinbase3bf2fa61bf9a65…501142097be87f

1 in → 1 out16.8500 XPM108 B

AWz5T9wo…KqSgM3j7

f4e045b30c8deb…82a84033f28fe8

1 in → 2 out19.8500 XPM192 B

AbLLL9Co…mJxR9e92 ANmEH1vj…9tpDJhNt

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.

1.428 × 10⁹¹(92-digit number)

14281836835430942678…26215624782740115479

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

1.428 × 10⁹¹(92-digit number)

14281836835430942678…26215624782740115479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.428 × 10⁹¹(92-digit number)

14281836835430942678…26215624782740115481

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

2.856 × 10⁹¹(92-digit number)

28563673670861885356…52431249565480230959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.856 × 10⁹¹(92-digit number)

28563673670861885356…52431249565480230961

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

5.712 × 10⁹¹(92-digit number)

57127347341723770712…04862499130960461919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.712 × 10⁹¹(92-digit number)

57127347341723770712…04862499130960461921

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

1.142 × 10⁹²(93-digit number)

11425469468344754142…09724998261920923839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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

CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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