Block #2,097,907

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2017, 2:35:19 AM · Difficulty 10.8691 · 4,716,289 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b70c2aa12a7934be3f6b2a05e375fec5a70671e697e66f321641902b23c5c16

View on Chainz ↗

Height

#2,097,907

Difficulty

10.869064

Transactions

Size

46.33 KB

Version

Bits

0ade7aff

Nonce

1,034,258,337

Timestamp

5/3/2017, 2:35:19 AM

Confirmations

4,716,289

Mined by

⛏️ P2SHAd2kkhE1xBFQKGGTD9XKyktGWadZUBT7ZK

Merkle Root

b9812461cf56d8d1649f93ae7a6fa298b3ed5c2202c31b413160f509e35f2003

Transactions (5)

Coinbase71b95d1875df9b…ffab8c708e2d14

1 in → 1 out8.9500 XPM109 B

Ad2kkhE1…dZUBT7ZK

0a65792419cf7e…83040e8ea65674

306 in → 1 out36.0000 XPM44.27 KB

AVaj27ki…Ntfy4Rjn

75e78d8317931a…33d26ca5f0c5c4

2 in → 1 out36.0000 XPM339 B

AVaj27ki…Ntfy4Rjn

71842134a5e0a1…3f9687a821c663

2 in → 1 out36.0000 XPM340 B

AVaj27ki…Ntfy4Rjn

97e9188dfdd2d9…43d117620c1653

8 in → 1 out28.0000 XPM1.20 KB

AUo7p97H…sJ9AyoTa

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.

2.939 × 10⁹⁶(97-digit number)

29396937924121874015…14712975985096601599

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

2.939 × 10⁹⁶(97-digit number)

29396937924121874015…14712975985096601599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.939 × 10⁹⁶(97-digit number)

29396937924121874015…14712975985096601601

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

5.879 × 10⁹⁶(97-digit number)

58793875848243748031…29425951970193203199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.879 × 10⁹⁶(97-digit number)

58793875848243748031…29425951970193203201

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

1.175 × 10⁹⁷(98-digit number)

11758775169648749606…58851903940386406399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.175 × 10⁹⁷(98-digit number)

11758775169648749606…58851903940386406401

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

2.351 × 10⁹⁷(98-digit number)

23517550339297499212…17703807880772812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.351 × 10⁹⁷(98-digit number)

23517550339297499212…17703807880772812801

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

4.703 × 10⁹⁷(98-digit number)

47035100678594998425…35407615761545625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.703 × 10⁹⁷(98-digit number)

47035100678594998425…35407615761545625601

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,097,907

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