Block #12,519

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 10:18:38 AM · Difficulty 7.7631 · 6,782,913 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

966a715520bf97bed4c897281ec803e23a3b7097198817984cf2d1866ac84826

View on Chainz ↗

Height

#12,519

Difficulty

7.763113

Transactions

Size

510 B

Version

Bits

07c35b64

Nonce

190

Timestamp

7/11/2013, 10:18:38 AM

Confirmations

6,782,913

Mined by

⛏️ P2SHAQqguvayJvZDgUprWnhmc94f34rq5wxyu5

Merkle Root

fbf25e9fa054491a49cebd440a64cb32642420ee234838abe4e837b98216a102

Transactions (3)

Coinbase24c515eda48e1e…32cd3e6aebeb73

1 in → 1 out16.5900 XPM108 B

AQqguvay…rq5wxyu5

cc94fa32633ff4…bb66db3fedbcfb

1 in → 1 out17.5100 XPM157 B

AU4AxAzL…y8DH19oQ

3774ab135fe628…b07c66611b74de

1 in → 1 out17.5000 XPM157 B

AdrE8sfc…odcy2d1B

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.

9.221 × 10⁸⁸(89-digit number)

92214647819779125272…50602911143351339109

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

9.221 × 10⁸⁸(89-digit number)

92214647819779125272…50602911143351339109

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.221 × 10⁸⁸(89-digit number)

92214647819779125272…50602911143351339111

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

1.844 × 10⁸⁹(90-digit number)

18442929563955825054…01205822286702678219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.844 × 10⁸⁹(90-digit number)

18442929563955825054…01205822286702678221

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

3.688 × 10⁸⁹(90-digit number)

36885859127911650108…02411644573405356439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.688 × 10⁸⁹(90-digit number)

36885859127911650108…02411644573405356441

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

7.377 × 10⁸⁹(90-digit number)

73771718255823300217…04823289146810712879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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