Block #39,213

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 1:08:49 PM · Difficulty 8.2908 · 6,750,723 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ddcc6e3934377f2b9185c4a1650a97f979f7926ce0f9640671eb276373ad064

View on Chainz ↗

Height

#39,213

Difficulty

8.290845

Transactions

Size

720 B

Version

Bits

084a74ce

Nonce

528

Timestamp

7/14/2013, 1:08:49 PM

Confirmations

6,750,723

Merkle Root

14e4b05ac84ecb5e716812951c3509cbe5d31ddeaaf76922c752ec76000b5906

Transactions (2)

Coinbased62884436ae9fe…e8490ca0a3df46

1 in → 1 out14.5400 XPM110 B

ALD4vzJs…GRCXP6ri

b75d8131bc2168…0bade67853b388

3 in → 2 out149.2326 XPM521 B

AKXG5vUo…7NyYyifR AY13aQNK…uZ92Hiaf

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.

7.067 × 10⁹¹(92-digit number)

70674382542068410981…22859546385889575129

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

7.067 × 10⁹¹(92-digit number)

70674382542068410981…22859546385889575129

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.067 × 10⁹¹(92-digit number)

70674382542068410981…22859546385889575131

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

1.413 × 10⁹²(93-digit number)

14134876508413682196…45719092771779150259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.413 × 10⁹²(93-digit number)

14134876508413682196…45719092771779150261

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

2.826 × 10⁹²(93-digit number)

28269753016827364392…91438185543558300519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.826 × 10⁹²(93-digit number)

28269753016827364392…91438185543558300521

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

5.653 × 10⁹²(93-digit number)

56539506033654728785…82876371087116601039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.653 × 10⁹²(93-digit number)

56539506033654728785…82876371087116601041

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

1.130 × 10⁹³(94-digit number)

11307901206730945757…65752742174233202079

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