Block #1,042,713

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2015, 6:26:30 AM · Difficulty 10.7232 · 5,760,796 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d37d12924736254663990940273ab54c60d9b668afc28254cf02117b7feb2ff4

View on Chainz ↗

Height

#1,042,713

Difficulty

10.723226

Transactions

Size

1.14 KB

Version

Bits

0ab92554

Nonce

488,057,923

Timestamp

5/3/2015, 6:26:30 AM

Confirmations

5,760,796

Mined by

⛏️ P2SHAXqGroFu8vMWQn44n3GTD9JWJcFTR6QRqP

Merkle Root

478d8406326a37ea642373ba40c658869fc8ee0cac807b5aa2357c26e8e09e2e

Transactions (4)

Coinbase76a8deb34efe74…3371866dae8cb6

1 in → 1 out8.7100 XPM109 B

AXqGroFu…FTR6QRqP

8510dcd72499ff…e7c6fd431d5a2a

2 in → 2 out15.8699 XPM373 B

AWpk8ztb…cdS7Quh7 AVuEzmJt…LGErqmd9

abe12c71ecbeda…e32d205e6dfbe8

2 in → 2 out10.7290 XPM374 B

Ae9drWdk…FnLTm9Pn AN3oyWk9…EHMaD85q

64d44781b62d39…ab802629c78bc7

1 in → 2 out7.5459 XPM225 B

APaYVt8e…rPF99zd2 AR3MvTUY…2KgKctJC

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.

1.086 × 10⁹⁴(95-digit number)

10860186908555854735…52743475651907576639

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

1.086 × 10⁹⁴(95-digit number)

10860186908555854735…52743475651907576639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.086 × 10⁹⁴(95-digit number)

10860186908555854735…52743475651907576641

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

2.172 × 10⁹⁴(95-digit number)

21720373817111709470…05486951303815153279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.172 × 10⁹⁴(95-digit number)

21720373817111709470…05486951303815153281

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

4.344 × 10⁹⁴(95-digit number)

43440747634223418941…10973902607630306559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.344 × 10⁹⁴(95-digit number)

43440747634223418941…10973902607630306561

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

8.688 × 10⁹⁴(95-digit number)

86881495268446837883…21947805215260613119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.688 × 10⁹⁴(95-digit number)

86881495268446837883…21947805215260613121

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

1.737 × 10⁹⁵(96-digit number)

17376299053689367576…43895610430521226239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.737 × 10⁹⁵(96-digit number)

17376299053689367576…43895610430521226241

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