Block #1,314,656

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/5/2015, 11:17:11 PM · Difficulty 10.8600 · 5,528,371 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c237590dc874bef48b2e75e59c644e6e55dc103e79996cf23308923c35e5ad26

View on Chainz ↗

Height

#1,314,656

Difficulty

10.859958

Transactions

Size

3.45 KB

Version

Bits

0adc2630

Nonce

195,956,247

Timestamp

11/5/2015, 11:17:11 PM

Confirmations

5,528,371

Mined by

⛏️ P2SHARsdWnLWFDAQ9iFiSLpDqTZvFwMMApTob9

Merkle Root

9a7657e7f7e9b4faf56fa1c1b534c39472cc5287012494ad3bbd936af2c5d806

Transactions (2)

Coinbased7082ce6ddc0e5…711ec938fd3349

1 in → 1 out9.1100 XPM110 B

ARsdWnLW…MMApTob9

c0a2a2eadfd516…a964800af1105f

22 in → 2 out1235.4255 XPM3.25 KB

AGdXLJNo…T6hJyCU4 AHccrvox…rZxQitpx

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.

6.757 × 10⁹³(94-digit number)

67572006650583161738…49960918382396564599

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

6.757 × 10⁹³(94-digit number)

67572006650583161738…49960918382396564599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.757 × 10⁹³(94-digit number)

67572006650583161738…49960918382396564601

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

1.351 × 10⁹⁴(95-digit number)

13514401330116632347…99921836764793129199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.351 × 10⁹⁴(95-digit number)

13514401330116632347…99921836764793129201

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

2.702 × 10⁹⁴(95-digit number)

27028802660233264695…99843673529586258399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.702 × 10⁹⁴(95-digit number)

27028802660233264695…99843673529586258401

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

5.405 × 10⁹⁴(95-digit number)

54057605320466529390…99687347059172516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.405 × 10⁹⁴(95-digit number)

54057605320466529390…99687347059172516801

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

1.081 × 10⁹⁵(96-digit number)

10811521064093305878…99374694118345033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.081 × 10⁹⁵(96-digit number)

10811521064093305878…99374694118345033601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,314,656

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