Block #1,349,720

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2015, 11:05:39 AM · Difficulty 10.8074 · 5,449,220 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0e09810b00dc94e8791b89fe290b942832eea46dbfb31dc2af011c9c4e73af7b

View on Chainz ↗

Height

#1,349,720

Difficulty

10.807399

Transactions

Size

935 B

Version

Bits

0aceb1b9

Nonce

88,664,407

Timestamp

12/1/2015, 11:05:39 AM

Confirmations

5,449,220

Mined by

⛏️ P2SHAdjaDZheJLsLRjFapHuQNgo9HJprSD1X4L

Merkle Root

3f4b454d3e6c85d334e348151f17791090e01936c0fa92ba63b3c011b8b6d9c1

Transactions (2)

Coinbasef13cea3c86eb5b…3f3c6c87de71bb

1 in → 1 out8.5600 XPM109 B

AdjaDZhe…prSD1X4L

6badd6284737dc…754cce946e88b9

1 in → 17 out131.7671 XPM736 B

AVM3B4py…gzRoNnok Aez935r7…J87g4y3B AXLkjH6Q…9wXKhR9V AXB2iJzr…VapWHkrP AKaacHEF…9KoZF1Nd

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.

6.868 × 10⁹³(94-digit number)

68680322159874944671…76198853388322557889

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

6.868 × 10⁹³(94-digit number)

68680322159874944671…76198853388322557889

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.868 × 10⁹³(94-digit number)

68680322159874944671…76198853388322557891

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

1.373 × 10⁹⁴(95-digit number)

13736064431974988934…52397706776645115779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.373 × 10⁹⁴(95-digit number)

13736064431974988934…52397706776645115781

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

2.747 × 10⁹⁴(95-digit number)

27472128863949977868…04795413553290231559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.747 × 10⁹⁴(95-digit number)

27472128863949977868…04795413553290231561

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

5.494 × 10⁹⁴(95-digit number)

54944257727899955736…09590827106580463119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.494 × 10⁹⁴(95-digit number)

54944257727899955736…09590827106580463121

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

1.098 × 10⁹⁵(96-digit number)

10988851545579991147…19181654213160926239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.098 × 10⁹⁵(96-digit number)

10988851545579991147…19181654213160926241

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