Block #2,315,095

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/30/2017, 2:09:53 AM · Difficulty 10.9072 · 4,500,896 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ecc651a8f0d3ca09a149a5b850c6c3aca65a8054571a2f90a5517206fd06647b

View on Chainz ↗

Height

#2,315,095

Difficulty

10.907227

Transactions

Size

757 B

Version

Bits

0ae84009

Nonce

265,816,939

Timestamp

9/30/2017, 2:09:53 AM

Confirmations

4,500,896

Mined by

⛏️ P2SHAZbHSUUmSu22bvuMDBcvSN4EfDoDaKTbu5

Merkle Root

5daefebf01b6214b0b5dc19c52606c03cd04fb85416ec8b18f89b7e271cd5104

Transactions (2)

Coinbase7c28124b6781bb…7c232b09d151cd

1 in → 1 out8.4000 XPM109 B

AZbHSUUm…oDaKTbu5

8551d8f22da8e2…3fc77135240f88

3 in → 3 out6010.5753 XPM557 B

AK1ZKL9u…KxUsPzJT AexxQu4T…H3bbSgnQ AcxhUhX6…N8N8w2tm

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.

1.588 × 10⁹⁶(97-digit number)

15884141291955530632…15622099607183155199

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

1.588 × 10⁹⁶(97-digit number)

15884141291955530632…15622099607183155199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.588 × 10⁹⁶(97-digit number)

15884141291955530632…15622099607183155201

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

3.176 × 10⁹⁶(97-digit number)

31768282583911061264…31244199214366310399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.176 × 10⁹⁶(97-digit number)

31768282583911061264…31244199214366310401

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

6.353 × 10⁹⁶(97-digit number)

63536565167822122528…62488398428732620799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.353 × 10⁹⁶(97-digit number)

63536565167822122528…62488398428732620801

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

1.270 × 10⁹⁷(98-digit number)

12707313033564424505…24976796857465241599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.270 × 10⁹⁷(98-digit number)

12707313033564424505…24976796857465241601

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

2.541 × 10⁹⁷(98-digit number)

25414626067128849011…49953593714930483199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.541 × 10⁹⁷(98-digit number)

25414626067128849011…49953593714930483201

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

5.082 × 10⁹⁷(98-digit number)

50829252134257698023…99907187429860966399

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 #2,315,095

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