Block #2,063,151

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2017, 8:14:47 AM · Difficulty 10.8532 · 4,777,787 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e9a854dda620b3e743948f62ba42af183ffb1756abe4ff2a50c69c446ad27f6

View on Chainz ↗

Height

#2,063,151

Difficulty

10.853196

Transactions

Size

724 B

Version

Bits

0ada6b0d

Nonce

210,485,915

Timestamp

4/9/2017, 8:14:47 AM

Confirmations

4,777,787

Mined by

⛏️ P2SHAPkeCqCVyhsTN8dmfaMQS5xSwajEoKbkEo

Merkle Root

1b2249aa159a7ec6e5809c00dd8354af0546f38872f134538b790fc21bc0d050

Transactions (2)

Coinbase9b00b5255008f4…a37ed0d719b7a1

1 in → 1 out8.4900 XPM109 B

APkeCqCV…jEoKbkEo

2697933a58871b…1b7517efc17fe3

3 in → 2 out14025.1210 XPM523 B

APtfmvfV…YPGFK5zH AMsEQha3…48JuU2x6

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.

3.789 × 10⁹⁸(99-digit number)

37899794247745973217…50655590753138114559

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

3.789 × 10⁹⁸(99-digit number)

37899794247745973217…50655590753138114559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.789 × 10⁹⁸(99-digit number)

37899794247745973217…50655590753138114561

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

7.579 × 10⁹⁸(99-digit number)

75799588495491946435…01311181506276229119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.579 × 10⁹⁸(99-digit number)

75799588495491946435…01311181506276229121

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

1.515 × 10⁹⁹(100-digit number)

15159917699098389287…02622363012552458239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.515 × 10⁹⁹(100-digit number)

15159917699098389287…02622363012552458241

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

3.031 × 10⁹⁹(100-digit number)

30319835398196778574…05244726025104916479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.031 × 10⁹⁹(100-digit number)

30319835398196778574…05244726025104916481

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

6.063 × 10⁹⁹(100-digit number)

60639670796393557148…10489452050209832959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.063 × 10⁹⁹(100-digit number)

60639670796393557148…10489452050209832961

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 #2,063,151

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