Block #2,495,196

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/29/2018, 1:33:06 AM · Difficulty 10.9735 · 4,343,287 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1c9262545a22adbac3e1f248078c1ac74632e3ab1278f8ed3004181b8fe72d1b

View on Chainz ↗

Height

#2,495,196

Difficulty

10.973491

Transactions

Size

574 B

Version

Bits

0af936b7

Nonce

100,498,459

Timestamp

1/29/2018, 1:33:06 AM

Confirmations

4,343,287

Mined by

⛏️ P2SHARSVaVcdZWK9frWfxbEsx2miu3V9Fu3uCj

Merkle Root

c93ef8cdcab986e7207cfebba99ff4712149312cf622f7036847b18ba2148048

Transactions (2)

Coinbase6b50928fd5bbcd…fdec958542720e

1 in → 1 out8.3000 XPM109 B

ARSVaVcd…V9Fu3uCj

51df1b8dc2c87c…3a22233527882e

2 in → 2 out13.6308 XPM375 B

ATyoKHjy…zCDbMmDr AcpKwKfN…6qjP7EVR

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.

7.676 × 10⁹³(94-digit number)

76766940137197169616…78912444298782810739

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

7.676 × 10⁹³(94-digit number)

76766940137197169616…78912444298782810739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.676 × 10⁹³(94-digit number)

76766940137197169616…78912444298782810741

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

1.535 × 10⁹⁴(95-digit number)

15353388027439433923…57824888597565621479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.535 × 10⁹⁴(95-digit number)

15353388027439433923…57824888597565621481

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

3.070 × 10⁹⁴(95-digit number)

30706776054878867846…15649777195131242959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.070 × 10⁹⁴(95-digit number)

30706776054878867846…15649777195131242961

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

6.141 × 10⁹⁴(95-digit number)

61413552109757735692…31299554390262485919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.141 × 10⁹⁴(95-digit number)

61413552109757735692…31299554390262485921

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

1.228 × 10⁹⁵(96-digit number)

12282710421951547138…62599108780524971839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.228 × 10⁹⁵(96-digit number)

12282710421951547138…62599108780524971841

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

2.456 × 10⁹⁵(96-digit number)

24565420843903094277…25198217561049943679

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 #2,495,196

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