Block #225,967

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/24/2013, 9:30:45 PM · Difficulty 9.9361 · 6,582,767 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

edc2e56c4a2becd031344e52385dfaccf9ac9eb874e26328882b419c2dd4cc2e

View on Chainz ↗

Height

#225,967

Difficulty

9.936083

Transactions

Size

3.64 KB

Version

Bits

09efa329

Nonce

180,643

Timestamp

10/24/2013, 9:30:45 PM

Confirmations

6,582,767

Mined by

⛏️ P2SHAYLrcFTXgeereKMsaYx1mswz1Hy2tWPkcR

Merkle Root

ddaf9c7f04530a8b5cd7ce9ab7c3119bac5e8f67045dfd977ef651b07339c251

Transactions (5)

Coinbase90bb1e76bb72b6…acc29950e0884b

1 in → 1 out10.1700 XPM109 B

AYLrcFTX…y2tWPkcR

2ec12668f1f8f4…16ae9597f310ec

1 in → 2 out1001.7277 XPM226 B

AJfYpYMb…UvLFxAs1 ARgwQBSn…hQJXCktr

454305da552745…149af11788d0f8

11 in → 1 out299.9900 XPM1.63 KB

AUxS45YF…yjEYccR3

2552d16f230d4e…af5084995462d9

2 in → 2 out10.7807 XPM376 B

AXJ4b3nV…M18ayaHD ALL6BtTJ…cp6j3qpk

c0f2f0094df70e…0e9b38c36ebce3

8 in → 2 out77.0235 XPM1.23 KB

Aa34UTN9…FJFh8bmn ALpthvGg…D1g5z4CT

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.

6.047 × 10⁹²(93-digit number)

60470421034779934553…27822428918968217599

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

6.047 × 10⁹²(93-digit number)

60470421034779934553…27822428918968217599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.047 × 10⁹²(93-digit number)

60470421034779934553…27822428918968217601

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

1.209 × 10⁹³(94-digit number)

12094084206955986910…55644857837936435199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.209 × 10⁹³(94-digit number)

12094084206955986910…55644857837936435201

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

2.418 × 10⁹³(94-digit number)

24188168413911973821…11289715675872870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.418 × 10⁹³(94-digit number)

24188168413911973821…11289715675872870401

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

4.837 × 10⁹³(94-digit number)

48376336827823947642…22579431351745740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.837 × 10⁹³(94-digit number)

48376336827823947642…22579431351745740801

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

9.675 × 10⁹³(94-digit number)

96752673655647895285…45158862703491481599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #225,967

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