Block #2,153,033

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/9/2017, 10:06:44 AM · Difficulty 10.9024 · 4,673,806 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ba8c380016774ae98daed7921f7601f83b8ab6cf3ed34c121de61ac973cc41d

View on Chainz ↗

Height

#2,153,033

Difficulty

10.902400

Transactions

Size

4.03 KB

Version

Bits

0ae703ad

Nonce

486,262,354

Timestamp

6/9/2017, 10:06:44 AM

Confirmations

4,673,806

Mined by

⛏️ P2SHAVHNyajzpcU15L6cYwesxNsEvdUMbStZhn

Merkle Root

1ebd59848b73026677ca05d0e29b1601126fbc867405a465a886e9afe579c72a

Transactions (2)

Coinbaseecb1a332925352…77ff95e2adb626

1 in → 1 out8.4400 XPM110 B

AVHNyajz…UMbStZhn

b3953b3b7e02a7…cc010f7808eb66

26 in → 2 out0.4792 XPM3.83 KB

AMXv76EL…ububrsQx AZtsbQK8…MT4UjHnt

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.

2.060 × 10⁹⁴(95-digit number)

20609938877503968120…64968166590344117759

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

2.060 × 10⁹⁴(95-digit number)

20609938877503968120…64968166590344117759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.060 × 10⁹⁴(95-digit number)

20609938877503968120…64968166590344117761

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

4.121 × 10⁹⁴(95-digit number)

41219877755007936240…29936333180688235519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.121 × 10⁹⁴(95-digit number)

41219877755007936240…29936333180688235521

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

8.243 × 10⁹⁴(95-digit number)

82439755510015872480…59872666361376471039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.243 × 10⁹⁴(95-digit number)

82439755510015872480…59872666361376471041

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

1.648 × 10⁹⁵(96-digit number)

16487951102003174496…19745332722752942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.648 × 10⁹⁵(96-digit number)

16487951102003174496…19745332722752942081

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

3.297 × 10⁹⁵(96-digit number)

32975902204006348992…39490665445505884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.297 × 10⁹⁵(96-digit number)

32975902204006348992…39490665445505884161

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 #2,153,033

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