Block #2,271,324

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/28/2017, 4:27:25 AM · Difficulty 10.9536 · 4,554,297 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65ea5d8472a7cb53070e9a9e0e5b80e23ca3aa99ffc80972484011f9dd471aed

View on Chainz ↗

Height

#2,271,324

Difficulty

10.953575

Transactions

Size

1.44 KB

Version

Bits

0af41d7e

Nonce

318,058,975

Timestamp

8/28/2017, 4:27:25 AM

Confirmations

4,554,297

Mined by

⛏️ P2SHAf1R5QhSJUkLSi9nQzsVMjW8i7HTWbgHV3

Merkle Root

9a30ceadfeee5edfa6ddcece0cd4b4ef2945442847552a65a9bca0c8d5140031

Transactions (4)

Coinbasefb421d8a4a0495…a095c0c9bbd3e5

1 in → 1 out8.3500 XPM110 B

Af1R5QhS…HTWbgHV3

24758216619412…0bc143cd633387

2 in → 2 out2222.2957 XPM374 B

AZG944aS…89TeiAR9 ASjQiqck…hpm5XyrR

a92ae24c67b263…3e4d168083bdf7

3 in → 2 out2099.4048 XPM523 B

AGyX4Mjh…vvtTpCRM AcyWcRuP…6p6D6YpU

b19b310d83db57…62eca88655f80e

2 in → 2 out1105.0357 XPM373 B

AWB2pgm1…xZtvRw5F AGLM8DMZ…3TtUfDDp

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.

9.443 × 10⁹⁴(95-digit number)

94430174171710804813…51954409309692269439

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

9.443 × 10⁹⁴(95-digit number)

94430174171710804813…51954409309692269439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.443 × 10⁹⁴(95-digit number)

94430174171710804813…51954409309692269441

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

1.888 × 10⁹⁵(96-digit number)

18886034834342160962…03908818619384538879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.888 × 10⁹⁵(96-digit number)

18886034834342160962…03908818619384538881

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

3.777 × 10⁹⁵(96-digit number)

37772069668684321925…07817637238769077759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.777 × 10⁹⁵(96-digit number)

37772069668684321925…07817637238769077761

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

7.554 × 10⁹⁵(96-digit number)

75544139337368643850…15635274477538155519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.554 × 10⁹⁵(96-digit number)

75544139337368643850…15635274477538155521

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

1.510 × 10⁹⁶(97-digit number)

15108827867473728770…31270548955076311039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.510 × 10⁹⁶(97-digit number)

15108827867473728770…31270548955076311041

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 #2,271,324

Cookie Preferences