Block #186,477

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 10:29:51 PM · Difficulty 9.8662 · 6,605,487 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf0831f4afce8102fb6fb53548eeb45b3f72bfae89b297871738e08651e03b39

View on Chainz ↗

Height

#186,477

Difficulty

9.866215

Transactions

Size

583 B

Version

Bits

09ddc040

Nonce

213,165

Timestamp

9/29/2013, 10:29:51 PM

Confirmations

6,605,487

Merkle Root

f81bcb8e8272980370bbba628023815c29e4cc7e3c09fc9dc47ff2597dacdf1e

Transactions (3)

Coinbasedfa2e400a42c2e…dba8e704daac11

1 in → 1 out10.2800 XPM109 B

AGuQwGL4…gG7pFtk8

ca65b26cd58a42…adee24d03ef1ad

1 in → 1 out10.3300 XPM158 B

AGhYPMso…zrjfZmXE

294583ce455a59…89f584ee6e6327

1 in → 2 out2.9136 XPM225 B

AXwKKGcU…yK2w3TwR AQ2M5ggz…2MgHdfuy

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.

7.939 × 10⁹⁶(97-digit number)

79393127275263691161…55868486545612647039

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

7.939 × 10⁹⁶(97-digit number)

79393127275263691161…55868486545612647039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.939 × 10⁹⁶(97-digit number)

79393127275263691161…55868486545612647041

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

1.587 × 10⁹⁷(98-digit number)

15878625455052738232…11736973091225294079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.587 × 10⁹⁷(98-digit number)

15878625455052738232…11736973091225294081

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

3.175 × 10⁹⁷(98-digit number)

31757250910105476464…23473946182450588159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.175 × 10⁹⁷(98-digit number)

31757250910105476464…23473946182450588161

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

6.351 × 10⁹⁷(98-digit number)

63514501820210952929…46947892364901176319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.351 × 10⁹⁷(98-digit number)

63514501820210952929…46947892364901176321

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

1.270 × 10⁹⁸(99-digit number)

12702900364042190585…93895784729802352639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.270 × 10⁹⁸(99-digit number)

12702900364042190585…93895784729802352641

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