Block #2,070,741

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2017, 11:09:47 AM · Difficulty 10.8596 · 4,769,136 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e2b3581701a03c536eec39c55a3b28b39cac7cc1f04d211ea17afa40561ac8c

View on Chainz ↗

Height

#2,070,741

Difficulty

10.859616

Transactions

Size

426 B

Version

Bits

0adc0fcc

Nonce

358,470,794

Timestamp

4/14/2017, 11:09:47 AM

Confirmations

4,769,136

Mined by

⛏️ P2SHAHTTqu8sMJQmtwgXHPngTtJHq3RsS7pXXJ

Merkle Root

0d7f9c9234a41975063a798b0f7f8eda665a739aba4acec00e205211a6135bbc

Transactions (2)

Coinbase6358c57f9bc44a…1b8c88829fb4e9

1 in → 1 out8.4800 XPM110 B

AHTTqu8s…RsS7pXXJ

151939a1b0b25b…b356bccf846b91

1 in → 2 out83217.7966 XPM226 B

ALMPewEv…QkLHqEuW AeXXViEd…tt5VHwoi

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.

9.748 × 10⁹³(94-digit number)

97484221167397211368…15035899896466024819

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

9.748 × 10⁹³(94-digit number)

97484221167397211368…15035899896466024819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.748 × 10⁹³(94-digit number)

97484221167397211368…15035899896466024821

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

1.949 × 10⁹⁴(95-digit number)

19496844233479442273…30071799792932049639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.949 × 10⁹⁴(95-digit number)

19496844233479442273…30071799792932049641

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

3.899 × 10⁹⁴(95-digit number)

38993688466958884547…60143599585864099279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.899 × 10⁹⁴(95-digit number)

38993688466958884547…60143599585864099281

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

7.798 × 10⁹⁴(95-digit number)

77987376933917769094…20287199171728198559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.798 × 10⁹⁴(95-digit number)

77987376933917769094…20287199171728198561

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

1.559 × 10⁹⁵(96-digit number)

15597475386783553818…40574398343456397119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.559 × 10⁹⁵(96-digit number)

15597475386783553818…40574398343456397121

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 #2,070,741

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