Block #215,083

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 8:53:55 PM · Difficulty 9.9250 · 6,581,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ddc3d7bbffeb2447d96f87de6ece670d02732d88095878ad6fafc2b0b77d25a4

View on Chainz ↗

Height

#215,083

Difficulty

9.924965

Transactions

Size

4.66 KB

Version

Bits

09ecca82

Nonce

1,164,781,211

Timestamp

10/17/2013, 8:53:55 PM

Confirmations

6,581,818

Mined by

⛏️ +HR`MAYdkvntTwj3BnBQaRYHStddbw7TCE18Zvb

Merkle Root

b893eaf1fc1d311e4e56c043a551845ff56e661e7a1fd1fecfdea53ea0211615

Transactions (1)

Coinbaseb893eaf1fc1d31…dea53ea0211615

1 in → 136 out10.0844 XPM4.58 KB

AYdkvntT…TCE18Zvb AXJbpPXX…UowxmF1S ASGXhVnp…gHNxHQYB AH8yR9wQ…3GmoUBGQ ANWEGnpn…gB9ZUftb

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.

1.459 × 10⁹³(94-digit number)

14595565712485019513…46397894627645539269

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

1.459 × 10⁹³(94-digit number)

14595565712485019513…46397894627645539269

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.459 × 10⁹³(94-digit number)

14595565712485019513…46397894627645539271

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

2.919 × 10⁹³(94-digit number)

29191131424970039027…92795789255291078539

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.919 × 10⁹³(94-digit number)

29191131424970039027…92795789255291078541

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

5.838 × 10⁹³(94-digit number)

58382262849940078054…85591578510582157079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.838 × 10⁹³(94-digit number)

58382262849940078054…85591578510582157081

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

1.167 × 10⁹⁴(95-digit number)

11676452569988015610…71183157021164314159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.167 × 10⁹⁴(95-digit number)

11676452569988015610…71183157021164314161

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

2.335 × 10⁹⁴(95-digit number)

23352905139976031221…42366314042328628319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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