Block #514,012

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 9:22:01 PM · Difficulty 10.8373 · 6,282,472 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbb76424979bfd50b324cca7c442b0b9abfa14e377f39eb8ec8db83cc89912df

View on Chainz ↗

Height

#514,012

Difficulty

10.837303

Transactions

Size

1.84 KB

Version

Bits

0ad65979

Nonce

97,450

Timestamp

4/27/2014, 9:22:01 PM

Confirmations

6,282,472

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6241c878a900380362ef5498c146faf4f865f7de5fd3a582e9746df67bf74074

Transactions (4)

Coinbaseb2f6419993141e…769e15720c1752

1 in → 18 out8.4994 XPM675 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j

cab53638cdc032…53ba393ef8bb83

3 in → 2 out22.9853 XPM522 B

AX1YDAyN…4nf2qN8K AaeQqgXc…EqTrTTtn

c5cb6b6b466d2f…a77d799514f093

2 in → 2 out7.4587 XPM373 B

ASHxq5u5…P6a3EF3E ARJ2qesV…ZM6WM5tJ

961e316e38069d…dbc9d1f52ffd69

1 in → 2 out4.4451 XPM225 B

AaTy68j8…9Kqx7tyQ ATjwywoV…ga9eRXwi

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.

1.770 × 10⁹⁶(97-digit number)

17707079149312602736…63473179361861024639

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

1.770 × 10⁹⁶(97-digit number)

17707079149312602736…63473179361861024639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.770 × 10⁹⁶(97-digit number)

17707079149312602736…63473179361861024641

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

3.541 × 10⁹⁶(97-digit number)

35414158298625205473…26946358723722049279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.541 × 10⁹⁶(97-digit number)

35414158298625205473…26946358723722049281

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

7.082 × 10⁹⁶(97-digit number)

70828316597250410946…53892717447444098559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.082 × 10⁹⁶(97-digit number)

70828316597250410946…53892717447444098561

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

1.416 × 10⁹⁷(98-digit number)

14165663319450082189…07785434894888197119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.416 × 10⁹⁷(98-digit number)

14165663319450082189…07785434894888197121

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

2.833 × 10⁹⁷(98-digit number)

28331326638900164378…15570869789776394239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.833 × 10⁹⁷(98-digit number)

28331326638900164378…15570869789776394241

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