Block #2,286,452

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/7/2017, 2:12:10 PM · Difficulty 10.9553 · 4,544,540 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd19754c364fdad382f6df0cd02bca90a82a53e1ecd8d5cebf88c7468a5787b5

View on Chainz ↗

Height

#2,286,452

Difficulty

10.955322

Transactions

Size

652 B

Version

Bits

0af48fff

Nonce

216,548,265

Timestamp

9/7/2017, 2:12:10 PM

Confirmations

4,544,540

Mined by

⛏️ P2SHAakLx8TNwDnTd8qcgk9W4r5xQoGCMbCK7p

Merkle Root

59a0db84d7c8cf22d5586f76240db92e5dd5e77f4362ec0f1e447f92c783be37

Transactions (3)

Coinbase6a3f8265f1aef1…a2997213b79c9d

1 in → 1 out8.3400 XPM110 B

AakLx8TN…GCMbCK7p

dbf67ae5a0bf21…b48c3a3c48d1fb

1 in → 2 out5834.9287 XPM226 B

AamTPMev…2zVD12wY AV9XeHFj…K1NnCqgN

8723b714dbf665…50c76e494457e2

1 in → 2 out5838.0200 XPM225 B

APTbc17U…jdHaS2m6 AS8Swa5k…emSJQqiE

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.

3.003 × 10⁹⁶(97-digit number)

30033572682106372114…65675210905879500799

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

3.003 × 10⁹⁶(97-digit number)

30033572682106372114…65675210905879500799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.003 × 10⁹⁶(97-digit number)

30033572682106372114…65675210905879500801

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

6.006 × 10⁹⁶(97-digit number)

60067145364212744229…31350421811759001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.006 × 10⁹⁶(97-digit number)

60067145364212744229…31350421811759001601

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

1.201 × 10⁹⁷(98-digit number)

12013429072842548845…62700843623518003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.201 × 10⁹⁷(98-digit number)

12013429072842548845…62700843623518003201

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

2.402 × 10⁹⁷(98-digit number)

24026858145685097691…25401687247036006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.402 × 10⁹⁷(98-digit number)

24026858145685097691…25401687247036006401

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

4.805 × 10⁹⁷(98-digit number)

48053716291370195383…50803374494072012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.805 × 10⁹⁷(98-digit number)

48053716291370195383…50803374494072012801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.610 × 10⁹⁷(98-digit number)

96107432582740390767…01606748988144025599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,286,452

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