Block #92,654

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/1/2013, 8:34:54 PM · Difficulty 9.2044 · 6,702,810 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

214414d081387cfd264fb57b3b4070ac70a6b6080a7b642fe2c8a7db3f122c91

View on Chainz ↗

Height

#92,654

Difficulty

9.204403

Transactions

Size

2.65 KB

Version

Bits

093453c3

Nonce

129,698

Timestamp

8/1/2013, 8:34:54 PM

Confirmations

6,702,810

Mined by

⛏️ P2SHAaHLE1xrKGkXketHnca4hWkrBwJMWqsYMr

Merkle Root

a2a49941f86e47f24d7883d6082d3200954500bb773f4263eac4712c11722f6f

Transactions (2)

Coinbase8d99ee8e791f92…352002656fff00

1 in → 1 out11.8200 XPM109 B

AaHLE1xr…JMWqsYMr

799cb7d130a710…1ac88074835aae

21 in → 3 out244.7000 XPM2.45 KB

AGfz3APU…kNJNtgfb ATzEHZ7a…2eAGweip AQ9VkUy6…TuxTAEug

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.

3.570 × 10¹¹³(114-digit number)

35707332103202047127…63330616704229112399

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

3.570 × 10¹¹³(114-digit number)

35707332103202047127…63330616704229112399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.570 × 10¹¹³(114-digit number)

35707332103202047127…63330616704229112401

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

7.141 × 10¹¹³(114-digit number)

71414664206404094255…26661233408458224799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.141 × 10¹¹³(114-digit number)

71414664206404094255…26661233408458224801

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

1.428 × 10¹¹⁴(115-digit number)

14282932841280818851…53322466816916449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.428 × 10¹¹⁴(115-digit number)

14282932841280818851…53322466816916449601

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

2.856 × 10¹¹⁴(115-digit number)

28565865682561637702…06644933633832899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.856 × 10¹¹⁴(115-digit number)

28565865682561637702…06644933633832899201

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

5.713 × 10¹¹⁴(115-digit number)

57131731365123275404…13289867267665798399

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