Block #317,125

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2013, 11:27:18 AM · Difficulty 10.1547 · 6,485,692 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fdaa549086bbe06d540c4dc8a79676f45be8903981331b6a9e5170632751ef9f

View on Chainz ↗

Height

#317,125

Difficulty

10.154720

Transactions

Size

3.05 KB

Version

Bits

0a279bc1

Nonce

629,963

Timestamp

12/17/2013, 11:27:18 AM

Confirmations

6,485,692

Mined by

⛏️ aR5%AWQBKr3YBNqdknh157YGqdQEjQsUA1Ehpd

Merkle Root

4f29c54b527f41b710f021baf45fbab9ea160ba37501973011c425f49c7014bb

Transactions (4)

Coinbase6bf2173c78f815…ea118c50d5bf67

1 in → 1 out9.6800 XPM97 B

AWQBKr3Y…sUA1Ehpd

1bf937157c7f02…632243a23c0f07

1 in → 4 out9.9100 XPM260 B

AeKNrjNj…1NEq95Ta ANFpe7j9…DDEt116M AVrzMBgN…EVKZMzxb AZ3PWPr3…T7o8gD2E

9339b1f2623e7d…2e946c7c091558

5 in → 2 out2.6052 XPM818 B

AJbdhjta…RDfJxWEn AMSiVTmf…LxGNFf5o

5a2818ae8c282a…e70c17625b820a

12 in → 2 out12.4953 XPM1.81 KB

AKbz7RfM…QhRq2n8q AK4BZ1un…5eHFgJDa

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.

7.269 × 10⁹³(94-digit number)

72697532557037436529…38137046774121355799

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

7.269 × 10⁹³(94-digit number)

72697532557037436529…38137046774121355799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.269 × 10⁹³(94-digit number)

72697532557037436529…38137046774121355801

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

1.453 × 10⁹⁴(95-digit number)

14539506511407487305…76274093548242711599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.453 × 10⁹⁴(95-digit number)

14539506511407487305…76274093548242711601

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

2.907 × 10⁹⁴(95-digit number)

29079013022814974611…52548187096485423199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.907 × 10⁹⁴(95-digit number)

29079013022814974611…52548187096485423201

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

5.815 × 10⁹⁴(95-digit number)

58158026045629949223…05096374192970846399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.815 × 10⁹⁴(95-digit number)

58158026045629949223…05096374192970846401

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

1.163 × 10⁹⁵(96-digit number)

11631605209125989844…10192748385941692799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.163 × 10⁹⁵(96-digit number)

11631605209125989844…10192748385941692801

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