Block #742,183

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/26/2014, 1:16:39 PM · Difficulty 10.9802 · 6,049,733 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

802ccaa0218664df0186b44c08292fd588d66c63fb9427ab572448a3c6bcbab0

View on Chainz ↗

Height

#742,183

Difficulty

10.980212

Transactions

Size

19.06 KB

Version

Bits

0afaef2d

Nonce

131,211,512

Timestamp

9/26/2014, 1:16:39 PM

Confirmations

6,049,733

Merkle Root

6ad20aca7e8728c672190618ac92311bf38921699d58138e3f0e68583a3c76ac

Transactions (2)

Coinbase471dcf08935162…392801bab26751

1 in → 1 out8.4800 XPM110 B

ANi3dR53…EbyRnBiQ

f533c0807e5ee6…ed226436e10474

130 in → 2 out400.0100 XPM18.87 KB

AWHsYQfu…ySJFJ7UD AW2VyPzy…PFuqv3iS

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.

1.763 × 10⁹⁵(96-digit number)

17638315152218453313…18717409161658695679

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

1.763 × 10⁹⁵(96-digit number)

17638315152218453313…18717409161658695679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.763 × 10⁹⁵(96-digit number)

17638315152218453313…18717409161658695681

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

3.527 × 10⁹⁵(96-digit number)

35276630304436906626…37434818323317391359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.527 × 10⁹⁵(96-digit number)

35276630304436906626…37434818323317391361

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

7.055 × 10⁹⁵(96-digit number)

70553260608873813252…74869636646634782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.055 × 10⁹⁵(96-digit number)

70553260608873813252…74869636646634782721

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

1.411 × 10⁹⁶(97-digit number)

14110652121774762650…49739273293269565439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.411 × 10⁹⁶(97-digit number)

14110652121774762650…49739273293269565441

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

2.822 × 10⁹⁶(97-digit number)

28221304243549525301…99478546586539130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.822 × 10⁹⁶(97-digit number)

28221304243549525301…99478546586539130881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.644 × 10⁹⁶(97-digit number)

56442608487099050602…98957093173078261759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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