Block #255,722

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 10:16:10 AM · Difficulty 9.9746 · 6,555,252 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23b7fd5f1a155ace52fccbf0609a2c466ca414131a03113c0a1a13ee00a8cfb6

View on Chainz ↗

Height

#255,722

Difficulty

9.974612

Transactions

Size

856 B

Version

Bits

09f9802c

Nonce

32,061

Timestamp

11/11/2013, 10:16:10 AM

Confirmations

6,555,252

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

61e8ac50765c7f845fd1482ad87e7b131fd59a2e08a323a74425cb9d74bcde70

Transactions (2)

Coinbasec114f3b21445c2…741b488669f135

1 in → 2 out10.0500 XPM141 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

7ce7d21b828618…386ebbf0549b7f

3 in → 8 out30.1500 XPM625 B

AJPry4G9…ost1kKHz ATmbcd5Q…KXVtig7M AUsL6VH6…Du8VQEdZ AeKNrjNj…1NEq95Ta AYiuPkxV…9nUvdUg1

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.

1.337 × 10⁹⁵(96-digit number)

13371448479730415218…25228183272428354959

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

1.337 × 10⁹⁵(96-digit number)

13371448479730415218…25228183272428354959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.337 × 10⁹⁵(96-digit number)

13371448479730415218…25228183272428354961

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

2.674 × 10⁹⁵(96-digit number)

26742896959460830437…50456366544856709919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.674 × 10⁹⁵(96-digit number)

26742896959460830437…50456366544856709921

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

5.348 × 10⁹⁵(96-digit number)

53485793918921660874…00912733089713419839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.348 × 10⁹⁵(96-digit number)

53485793918921660874…00912733089713419841

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

1.069 × 10⁹⁶(97-digit number)

10697158783784332174…01825466179426839679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.069 × 10⁹⁶(97-digit number)

10697158783784332174…01825466179426839681

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

2.139 × 10⁹⁶(97-digit number)

21394317567568664349…03650932358853679359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.139 × 10⁹⁶(97-digit number)

21394317567568664349…03650932358853679361

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

Block #255,722

Cookie Preferences