Block #2,271,858

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/28/2017, 12:34:23 PM · Difficulty 10.9540 · 4,555,350 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7781e0e4426cf5ba77d22207c1d27c45d4b680053ec38f61ac5771961cadfd10

View on Chainz ↗

Height

#2,271,858

Difficulty

10.954020

Transactions

Size

574 B

Version

Bits

0af43aa3

Nonce

787,367,946

Timestamp

8/28/2017, 12:34:23 PM

Confirmations

4,555,350

Mined by

⛏️ P2SHAdJR6VSECGjGCvrp5Kqc13ZWA7Zwh5Qkcu

Merkle Root

6edabc0c3beba99253b3b3d4c6677582890d3552b72900e76ace512b0829f6d8

Transactions (2)

Coinbasec2e4efb7e334f3…d04f18d6d6f226

1 in → 1 out8.3300 XPM110 B

AdJR6VSE…Zwh5Qkcu

c0040a7e77049c…6dd1105d756641

2 in → 2 out2120.3600 XPM373 B

ARaNCeSx…b8M3uhxY ASXzjgV8…NbGQT1dg

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.

1.243 × 10⁹⁸(99-digit number)

12435125748621247019…81047759377122344959

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

1.243 × 10⁹⁸(99-digit number)

12435125748621247019…81047759377122344959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.243 × 10⁹⁸(99-digit number)

12435125748621247019…81047759377122344961

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

2.487 × 10⁹⁸(99-digit number)

24870251497242494038…62095518754244689919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.487 × 10⁹⁸(99-digit number)

24870251497242494038…62095518754244689921

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

4.974 × 10⁹⁸(99-digit number)

49740502994484988077…24191037508489379839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.974 × 10⁹⁸(99-digit number)

49740502994484988077…24191037508489379841

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

9.948 × 10⁹⁸(99-digit number)

99481005988969976154…48382075016978759679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.948 × 10⁹⁸(99-digit number)

99481005988969976154…48382075016978759681

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

1.989 × 10⁹⁹(100-digit number)

19896201197793995230…96764150033957519359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.989 × 10⁹⁹(100-digit number)

19896201197793995230…96764150033957519361

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 #2,271,858

Cookie Preferences