Block #337,891

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/1/2014, 12:57:34 AM · Difficulty 10.1278 · 6,461,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7915bdeb31a44ee220468551085f58fadea1fb1ef5a66a199b2c06c5331459b4

View on Chainz ↗

Height

#337,891

Difficulty

10.127770

Transactions

Size

4.73 KB

Version

Bits

0a20b585

Nonce

17,192

Timestamp

1/1/2014, 12:57:34 AM

Confirmations

6,461,131

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7f67ba943329c95db2d3f8b9fe0d0b59580f8c12b33fe208a8071c37cf71ca93

Transactions (5)

Coinbaseba1cae9931f99f…c56b9c079b3af0

1 in → 1 out9.8000 XPM110 B

AeKNrjNj…1NEq95Ta

d57c6e0de56714…99c3a5574ccf92

26 in → 2 out100.0104 XPM3.73 KB

AazypqVZ…F5Qvr1Y8 AQ6uXdAu…q5s5Fs7F

563f92246b0918…46d6a00b14b873

2 in → 2 out10.2358 XPM373 B

AXJVATiG…MyCEPKgG AbB12zLb…wX14BLdx

7cdf7bd1a76edb…c22d02df6f0985

1 in → 2 out5.5332 XPM226 B

APjuLQBx…oP8jLMWm Ae1w8wLv…7iWbiEGf

65f1e15f2eee6f…59ea9f0a1310dd

1 in → 2 out1.4838 XPM226 B

Ac1tJckR…PnJfMhfu ATGiFHiu…L1hZjJvT

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.

1.378 × 10⁹⁷(98-digit number)

13781987567497082420…13758510909810405119

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

1.378 × 10⁹⁷(98-digit number)

13781987567497082420…13758510909810405119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.378 × 10⁹⁷(98-digit number)

13781987567497082420…13758510909810405121

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

2.756 × 10⁹⁷(98-digit number)

27563975134994164841…27517021819620810239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.756 × 10⁹⁷(98-digit number)

27563975134994164841…27517021819620810241

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

5.512 × 10⁹⁷(98-digit number)

55127950269988329683…55034043639241620479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.512 × 10⁹⁷(98-digit number)

55127950269988329683…55034043639241620481

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

1.102 × 10⁹⁸(99-digit number)

11025590053997665936…10068087278483240959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.102 × 10⁹⁸(99-digit number)

11025590053997665936…10068087278483240961

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

2.205 × 10⁹⁸(99-digit number)

22051180107995331873…20136174556966481919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.205 × 10⁹⁸(99-digit number)

22051180107995331873…20136174556966481921

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