Block #1,043,671

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2015, 10:46:19 PM · Difficulty 10.7220 · 5,748,147 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

64e94a5e1e6c263a6252f9c4c3e2cf5fb35c1711ad7f4b8faaaf847e5862baf0

View on Chainz ↗

Height

#1,043,671

Difficulty

10.722049

Transactions

Size

571 B

Version

Bits

0ab8d834

Nonce

1,111,130,620

Timestamp

5/3/2015, 10:46:19 PM

Confirmations

5,748,147

Merkle Root

3eb3b8b971732a16259fd5a04f6d87229fbae7dfff35e62f9a8737144f99a6b8

Transactions (2)

Coinbase7b6e221adef856…84c7b550155759

1 in → 1 out8.6900 XPM109 B

AJUXy9fc…RfxpAX5b

4d845ffc6ca481…5520beb630408d

2 in → 2 out15.1889 XPM373 B

Ae9drWdk…FnLTm9Pn AZCwwXxs…Hci4Ufoh

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.

7.808 × 10⁹¹(92-digit number)

78082187777072129579…99658787129313387479

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

7.808 × 10⁹¹(92-digit number)

78082187777072129579…99658787129313387479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.808 × 10⁹¹(92-digit number)

78082187777072129579…99658787129313387481

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

1.561 × 10⁹²(93-digit number)

15616437555414425915…99317574258626774959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.561 × 10⁹²(93-digit number)

15616437555414425915…99317574258626774961

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

3.123 × 10⁹²(93-digit number)

31232875110828851831…98635148517253549919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.123 × 10⁹²(93-digit number)

31232875110828851831…98635148517253549921

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

6.246 × 10⁹²(93-digit number)

62465750221657703663…97270297034507099839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.246 × 10⁹²(93-digit number)

62465750221657703663…97270297034507099841

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

1.249 × 10⁹³(94-digit number)

12493150044331540732…94540594069014199679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.249 × 10⁹³(94-digit number)

12493150044331540732…94540594069014199681

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