Block #1,315,803

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/6/2015, 4:41:11 PM · Difficulty 10.8628 · 5,500,622 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d79fa374a5cf677331b233c6b915793fe2bb5f592d74ed9af2fe83485ed3e1e

View on Chainz ↗

Height

#1,315,803

Difficulty

10.862804

Transactions

Size

4.02 KB

Version

Bits

0adce0bc

Nonce

606,651,084

Timestamp

11/6/2015, 4:41:11 PM

Confirmations

5,500,622

Mined by

⛏️ P2SHAJ1ZVY1fvMzhMwfPtwcZjnJAMPsfZEZRRD

Merkle Root

2591f5df95c4082ba737a84d1290fb7d5bebcdcee892681b0f9ebc115234de6e

Transactions (2)

Coinbase583840c17aea0e…048241f187c52d

1 in → 1 out8.5100 XPM110 B

AJ1ZVY1f…sfZEZRRD

5e82595b0fd70a…3eb470ece21fe4

26 in → 2 out24.3866 XPM3.83 KB

AZN3ZN8C…X6m3Fwnk ALsN5neD…LQtpQCCS

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.

4.861 × 10⁹¹(92-digit number)

48614054748224658787…64485747043248985599

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

4.861 × 10⁹¹(92-digit number)

48614054748224658787…64485747043248985599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.861 × 10⁹¹(92-digit number)

48614054748224658787…64485747043248985601

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

9.722 × 10⁹¹(92-digit number)

97228109496449317575…28971494086497971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.722 × 10⁹¹(92-digit number)

97228109496449317575…28971494086497971201

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

1.944 × 10⁹²(93-digit number)

19445621899289863515…57942988172995942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.944 × 10⁹²(93-digit number)

19445621899289863515…57942988172995942401

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

3.889 × 10⁹²(93-digit number)

38891243798579727030…15885976345991884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.889 × 10⁹²(93-digit number)

38891243798579727030…15885976345991884801

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

7.778 × 10⁹²(93-digit number)

77782487597159454060…31771952691983769599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.778 × 10⁹²(93-digit number)

77782487597159454060…31771952691983769601

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 #1,315,803

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