Block #2,120,046

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2017, 2:59:30 AM · Difficulty 10.9118 · 4,723,003 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a751d858ff619561334cfb6b47b63ca87111dec689d3e435d123697aeee906cf

View on Chainz ↗

Height

#2,120,046

Difficulty

10.911760

Transactions

Size

621 B

Version

Bits

0ae9691d

Nonce

934,354,117

Timestamp

5/17/2017, 2:59:30 AM

Confirmations

4,723,003

Mined by

⛏️ P2SHATSqBZ1jASMNjndDAzAcxK7pPjZ3xWZs6B

Merkle Root

bf2297ea610eda8ebde987062361ed411a86b8a5f3d68445df5964a3cdf3face

Transactions (3)

Coinbasee5df0fe85396e9…8ff7ddd3a62ec8

1 in → 1 out8.4100 XPM110 B

ATSqBZ1j…Z3xWZs6B

2ec4c1d0ea7e62…4ec33e019dfb9a

1 in → 1 out7.9700 XPM193 B

AZo7Crp5…RLcoyg17

40adb7e32daec9…58fc78d9c4771d

1 in → 2 out93.0400 XPM227 B

AbqXRqrX…93pFH86f AeXQdh57…LuPjDvHv

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.

8.385 × 10⁹⁷(98-digit number)

83857185579828071806…26084996931506585599

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

8.385 × 10⁹⁷(98-digit number)

83857185579828071806…26084996931506585599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.385 × 10⁹⁷(98-digit number)

83857185579828071806…26084996931506585601

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

1.677 × 10⁹⁸(99-digit number)

16771437115965614361…52169993863013171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.677 × 10⁹⁸(99-digit number)

16771437115965614361…52169993863013171201

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

3.354 × 10⁹⁸(99-digit number)

33542874231931228722…04339987726026342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.354 × 10⁹⁸(99-digit number)

33542874231931228722…04339987726026342401

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

6.708 × 10⁹⁸(99-digit number)

67085748463862457445…08679975452052684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.708 × 10⁹⁸(99-digit number)

67085748463862457445…08679975452052684801

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

1.341 × 10⁹⁹(100-digit number)

13417149692772491489…17359950904105369599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.341 × 10⁹⁹(100-digit number)

13417149692772491489…17359950904105369601

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 #2,120,046

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