Block #318,259

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/18/2013, 5:57:12 AM · Difficulty 10.1594 · 6,478,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

42959edf07bf099886ad91a8307d74b394ebb3b62287ccac019cd3b0daa55fb0

View on Chainz ↗

Height

#318,259

Difficulty

10.159433

Transactions

Size

2.91 KB

Version

Bits

0a28d094

Nonce

103,799

Timestamp

12/18/2013, 5:57:12 AM

Confirmations

6,478,186

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

1303011a3d54bdac74a4d2246c3b9ef95b50ba505a906a9931b8723f67cdcd69

Transactions (4)

Coinbase322647f14e97cf…9cb5e4ed1b47f0

1 in → 1 out9.7184 XPM110 B

AeKNrjNj…1NEq95Ta

42192f9525d9df…830cf3a6329e7a

2 in → 2 out35.9890 XPM373 B

AMSj35t4…12GtKPQA AHJQKp8R…P7GxA3dv

82219335db8ea8…2d2c94cba01f8d

4 in → 11 out31.1160 XPM873 B

AbiqL7S1…fT5KvTUs AeBSqG1J…UrHa7Jvn AbBfJxdv…5LhhDvme AcpjiZSC…TNRJHCGa ARRGt2ew…tqppTAg9

36e6e9aebfc6a9…7c0857bdf4310d

10 in → 1 out3.1000 XPM1.49 KB

AS3jR6dp…mJkqFNQP

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.

9.868 × 10¹⁰³(104-digit number)

98680146967740834484…04673403978311557119

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

9.868 × 10¹⁰³(104-digit number)

98680146967740834484…04673403978311557119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.868 × 10¹⁰³(104-digit number)

98680146967740834484…04673403978311557121

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

1.973 × 10¹⁰⁴(105-digit number)

19736029393548166896…09346807956623114239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.973 × 10¹⁰⁴(105-digit number)

19736029393548166896…09346807956623114241

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

3.947 × 10¹⁰⁴(105-digit number)

39472058787096333793…18693615913246228479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.947 × 10¹⁰⁴(105-digit number)

39472058787096333793…18693615913246228481

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

7.894 × 10¹⁰⁴(105-digit number)

78944117574192667587…37387231826492456959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.894 × 10¹⁰⁴(105-digit number)

78944117574192667587…37387231826492456961

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

1.578 × 10¹⁰⁵(106-digit number)

15788823514838533517…74774463652984913919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.578 × 10¹⁰⁵(106-digit number)

15788823514838533517…74774463652984913921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.157 × 10¹⁰⁵(106-digit number)

31577647029677067034…49548927305969827839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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