Block #313,323

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/15/2013, 10:16:41 AM · Difficulty 9.9961 · 6,504,418 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7566abeb2889d53886b8297a51cf065f2183a0f3e6ecd0f7613061aad7ce30eb

View on Chainz ↗

Height

#313,323

Difficulty

9.996087

Transactions

Size

1.22 KB

Version

Bits

09feff93

Nonce

432,688

Timestamp

12/15/2013, 10:16:41 AM

Confirmations

6,504,418

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5c0f9e038d6ddcd8baff8b033c7991b098f745fe55429db30368eb66465f0e0e

Transactions (5)

Coinbase5e06de6435d89b…07209731d611d9

1 in → 1 out10.0300 XPM110 B

AeKNrjNj…1NEq95Ta

4e35c9bee7a7fe…1f5a05fa41ff37

1 in → 2 out6.8836 XPM225 B

Aazu5MN1…Y2mhGkmp AZwyMUeE…rxMQeLU7

d2432bea84cde4…01d288ea4e0aee

1 in → 2 out6.8950 XPM226 B

ATHR6oPB…CWcCmaGW AQATwGZK…bRX1N6QZ

34dce13ec9cedf…dcbaad7db92249

1 in → 2 out4.7396 XPM226 B

AYSP2GPX…NeDbActP ALrxtRZB…pgpnxSCZ

0773354db57bf7…4f654c527071ad

2 in → 2 out5.0538 XPM374 B

AcQvZa25…ohwWjcDh AQQEvpo8…1vPw23n6

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.

1.033 × 10⁹⁴(95-digit number)

10336530039124784646…40704163943559107279

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

1.033 × 10⁹⁴(95-digit number)

10336530039124784646…40704163943559107279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.033 × 10⁹⁴(95-digit number)

10336530039124784646…40704163943559107281

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

2.067 × 10⁹⁴(95-digit number)

20673060078249569292…81408327887118214559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.067 × 10⁹⁴(95-digit number)

20673060078249569292…81408327887118214561

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

4.134 × 10⁹⁴(95-digit number)

41346120156499138584…62816655774236429119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.134 × 10⁹⁴(95-digit number)

41346120156499138584…62816655774236429121

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

8.269 × 10⁹⁴(95-digit number)

82692240312998277168…25633311548472858239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.269 × 10⁹⁴(95-digit number)

82692240312998277168…25633311548472858241

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

1.653 × 10⁹⁵(96-digit number)

16538448062599655433…51266623096945716479

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

Block #313,323

Cookie Preferences