Block #2,667,334

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/18/2018, 8:36:19 PM · Difficulty 11.6705 · 4,165,880 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce34aba68c6e60a315ca7a5ad21e98aa6a15d508b8e39c489f0b6866a983057b

View on Chainz ↗

Height

#2,667,334

Difficulty

11.670536

Transactions

Size

609 B

Version

Bits

0baba83a

Nonce

487,621,388

Timestamp

5/18/2018, 8:36:19 PM

Confirmations

4,165,880

Mined by

⛏️ P2SHAZekqjqW1PspaTRJBDtsR1bW4iy3aiB2gg

Merkle Root

f93fbdcef574620525fc0817b96841c67da16e8b3614a0dc4e31aa4664859383

Transactions (2)

Coinbase6bee300aa37549…9637ae38335cdd

1 in → 1 out7.3400 XPM110 B

AZekqjqW…y3aiB2gg

99e609e3d7a4eb…345281e3cee527

2 in → 3 out384.1620 XPM409 B

AaxAx69M…J6ooCxWR AdepddBi…eU9B97yt AJzq1stF…M2ZPubtX

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.

2.310 × 10⁹⁵(96-digit number)

23105204640656141470…45004241829235056639

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

2.310 × 10⁹⁵(96-digit number)

23105204640656141470…45004241829235056639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.310 × 10⁹⁵(96-digit number)

23105204640656141470…45004241829235056641

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

4.621 × 10⁹⁵(96-digit number)

46210409281312282941…90008483658470113279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.621 × 10⁹⁵(96-digit number)

46210409281312282941…90008483658470113281

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

9.242 × 10⁹⁵(96-digit number)

92420818562624565883…80016967316940226559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.242 × 10⁹⁵(96-digit number)

92420818562624565883…80016967316940226561

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

1.848 × 10⁹⁶(97-digit number)

18484163712524913176…60033934633880453119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.848 × 10⁹⁶(97-digit number)

18484163712524913176…60033934633880453121

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

3.696 × 10⁹⁶(97-digit number)

36968327425049826353…20067869267760906239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.696 × 10⁹⁶(97-digit number)

36968327425049826353…20067869267760906241

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

7.393 × 10⁹⁶(97-digit number)

73936654850099652707…40135738535521812479

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

Block #2,667,334

Cookie Preferences