Block #151,551

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 6:05:53 PM · Difficulty 9.8611 · 6,658,992 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1018896b224f704f8c182f19112cf22f677e288ec2e1c87d98350616cbda58bb

View on Chainz ↗

Height

#151,551

Difficulty

9.861079

Transactions

Size

720 B

Version

Bits

09dc6fa7

Nonce

37,179

Timestamp

9/5/2013, 6:05:53 PM

Confirmations

6,658,992

Mined by

⛏️ P2SHAJkcBGvuouoWiEQ4AmFvGo3qwPhSNwhPED

Merkle Root

0bb2bc592b8039f86b889d9fb3ecf493df525235052d6e1843c580268a401976

Transactions (2)

Coinbase1bb379b19a85c0…2221ee471e788a

1 in → 1 out10.2800 XPM109 B

AJkcBGvu…hSNwhPED

320f406c5f844b…d1ef542dc57883

3 in → 2 out150.0102 XPM522 B

AT4aqcDT…GFFKgRYC ANs6RLmi…c8sdUqec

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.

1.153 × 10⁹²(93-digit number)

11530486662364840324…08323824785830004479

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

1.153 × 10⁹²(93-digit number)

11530486662364840324…08323824785830004479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.153 × 10⁹²(93-digit number)

11530486662364840324…08323824785830004481

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

2.306 × 10⁹²(93-digit number)

23060973324729680648…16647649571660008959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.306 × 10⁹²(93-digit number)

23060973324729680648…16647649571660008961

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

4.612 × 10⁹²(93-digit number)

46121946649459361296…33295299143320017919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.612 × 10⁹²(93-digit number)

46121946649459361296…33295299143320017921

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

9.224 × 10⁹²(93-digit number)

92243893298918722593…66590598286640035839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.224 × 10⁹²(93-digit number)

92243893298918722593…66590598286640035841

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

1.844 × 10⁹³(94-digit number)

18448778659783744518…33181196573280071679

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

Block #151,551

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