Block #148,089

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/3/2013, 12:32:50 PM · Difficulty 9.8539 · 6,644,702 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

919ec8cc73e6925a4a287929c48a8ed1b41901358f9b7280d789398786840fad

View on Chainz ↗

Height

#148,089

Difficulty

9.853874

Transactions

Size

198 B

Version

Bits

09da977c

Nonce

86,789

Timestamp

9/3/2013, 12:32:50 PM

Confirmations

6,644,702

Merkle Root

fd20ba143b846a6abdb08296c446a4c8b3e3d558874c7ebb1780af090b4fccce

Transactions (1)

Coinbasefd20ba143b846a…80af090b4fccce

1 in → 1 out10.2800 XPM109 B

AcrXkx8M…tKGb6K4t

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.

6.462 × 10⁹²(93-digit number)

64626013742112973026…68865388649982573119

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

6.462 × 10⁹²(93-digit number)

64626013742112973026…68865388649982573119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.462 × 10⁹²(93-digit number)

64626013742112973026…68865388649982573121

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

1.292 × 10⁹³(94-digit number)

12925202748422594605…37730777299965146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.292 × 10⁹³(94-digit number)

12925202748422594605…37730777299965146241

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

2.585 × 10⁹³(94-digit number)

25850405496845189210…75461554599930292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.585 × 10⁹³(94-digit number)

25850405496845189210…75461554599930292481

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

5.170 × 10⁹³(94-digit number)

51700810993690378420…50923109199860584959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.170 × 10⁹³(94-digit number)

51700810993690378420…50923109199860584961

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

1.034 × 10⁹⁴(95-digit number)

10340162198738075684…01846218399721169919

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