Block #2,297,156

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/15/2017, 1:33:54 PM · Difficulty 10.9483 · 4,543,157 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c028b84b04a2be727f7d547d2e56be6a352115b953a7b14965c9079e229db1d1

View on Chainz ↗

Height

#2,297,156

Difficulty

10.948258

Transactions

Size

1.14 KB

Version

Bits

0af2c10e

Nonce

1,063,758,554

Timestamp

9/15/2017, 1:33:54 PM

Confirmations

4,543,157

Mined by

⛏️ P2SHAVjJbMdpXBhvJDNsFgz55v5h6CgpinFVjx

Merkle Root

0ca0aea30fd82a6f78ad19f9ae5c136c335e2309887379e255064e407564eee1

Transactions (2)

Coinbase997783c57069fd…7ecc1f8bb1dddd

1 in → 1 out8.3400 XPM109 B

AVjJbMdp…gpinFVjx

6a3dd0987c5510…006683d3681d99

6 in → 2 out580.1974 XPM968 B

APpFqTh1…LZ7MbhHg AeoYRFM9…akPhgXp7

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.

1.969 × 10⁹⁷(98-digit number)

19695380056372882884…15914775702637854719

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

1.969 × 10⁹⁷(98-digit number)

19695380056372882884…15914775702637854719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.969 × 10⁹⁷(98-digit number)

19695380056372882884…15914775702637854721

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

3.939 × 10⁹⁷(98-digit number)

39390760112745765769…31829551405275709439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.939 × 10⁹⁷(98-digit number)

39390760112745765769…31829551405275709441

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

7.878 × 10⁹⁷(98-digit number)

78781520225491531538…63659102810551418879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.878 × 10⁹⁷(98-digit number)

78781520225491531538…63659102810551418881

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

1.575 × 10⁹⁸(99-digit number)

15756304045098306307…27318205621102837759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.575 × 10⁹⁸(99-digit number)

15756304045098306307…27318205621102837761

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

3.151 × 10⁹⁸(99-digit number)

31512608090196612615…54636411242205675519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.151 × 10⁹⁸(99-digit number)

31512608090196612615…54636411242205675521

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

6.302 × 10⁹⁸(99-digit number)

63025216180393225231…09272822484411351039

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 #2,297,156

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