Block #2,237,207

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/4/2017, 10:22:40 PM · Difficulty 10.9463 · 4,604,821 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

73b060c931f9eabc9930461ee9578ce2b3ef26d1983a0ca8cd5635ee04fa718a

View on Chainz ↗

Height

#2,237,207

Difficulty

10.946260

Transactions

Size

1018 B

Version

Bits

0af23e1a

Nonce

1,856,498,547

Timestamp

8/4/2017, 10:22:40 PM

Confirmations

4,604,821

Mined by

⛏️ P2SHAFokNmVKuLB8gJavtZdA2qVQsyn5mY5Cff

Merkle Root

2a380a0079a2bb356aaf4e7b6ce368e905212fafb5450a8ca3364dc3207465b8

Transactions (2)

Coinbaseb2be9a75dcaa73…08963b3aa8ee1f

1 in → 1 out8.3400 XPM110 B

AFokNmVK…n5mY5Cff

778d522dd2d16a…c4fb7a219c6759

5 in → 2 out1511.6890 XPM817 B

AbrVa3wd…PPYNhzzV AM43k1nt…YL3cZrpR

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.

7.653 × 10⁹⁶(97-digit number)

76532279483497451012…54619121200990064639

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

7.653 × 10⁹⁶(97-digit number)

76532279483497451012…54619121200990064639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.653 × 10⁹⁶(97-digit number)

76532279483497451012…54619121200990064641

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

1.530 × 10⁹⁷(98-digit number)

15306455896699490202…09238242401980129279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.530 × 10⁹⁷(98-digit number)

15306455896699490202…09238242401980129281

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

3.061 × 10⁹⁷(98-digit number)

30612911793398980405…18476484803960258559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.061 × 10⁹⁷(98-digit number)

30612911793398980405…18476484803960258561

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

6.122 × 10⁹⁷(98-digit number)

61225823586797960810…36952969607920517119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.122 × 10⁹⁷(98-digit number)

61225823586797960810…36952969607920517121

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

1.224 × 10⁹⁸(99-digit number)

12245164717359592162…73905939215841034239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.224 × 10⁹⁸(99-digit number)

12245164717359592162…73905939215841034241

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 #2,237,207

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