Block #2,083,927

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2017, 7:15:17 AM · Difficulty 10.8722 · 4,730,463 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf8f848c6e764e32ecac535dd5f9de6527c056b14fd366d8f6e93d425c4e9058

View on Chainz ↗

Height

#2,083,927

Difficulty

10.872197

Transactions

Size

7.98 KB

Version

Bits

0adf4850

Nonce

1,436,433,067

Timestamp

4/23/2017, 7:15:17 AM

Confirmations

4,730,463

Mined by

⛏️ P2SHAXdSf5DFwKdsHTd2PRqfitRqnqmAjPumLN

Merkle Root

bee48a7acfa5bc3b87411d92319a921227dea8d10ba18672b20fd8acc00710e3

Transactions (4)

Coinbase95f04f9caf1d50…86d330a677ca19

1 in → 1 out8.5400 XPM109 B

AXdSf5DF…mAjPumLN

7f0d9b339af7f6…8b00c4df4c98eb

4 in → 1 out2919.9900 XPM637 B

AXo7xgdi…w5m2AWXo

baa63f4d7e13f1…c964baf406ddf7

1 in → 101 out30.9639 XPM3.51 KB

AUnRnrYD…8nqiASKn AdEPXFN6…AVShB71f AWRDx5ty…rftCrhV9 AeeHBAdf…vc3DLc31 AGhXe3Tv…5H1SpqbJ

74d543d7c4825c…038f743e90c27d

2 in → 101 out29.9580 XPM3.65 KB

ANeARd72…DBXKN9cK AJWmzCGZ…cvTb1AmT AUt3iVGP…FJ1Gi5Bu AU2BK16s…oBqAzsDF AHLkr8VW…72s1bCzw

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.

6.565 × 10⁹⁵(96-digit number)

65653137560523883138…07481915617443107199

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

6.565 × 10⁹⁵(96-digit number)

65653137560523883138…07481915617443107199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.565 × 10⁹⁵(96-digit number)

65653137560523883138…07481915617443107201

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

1.313 × 10⁹⁶(97-digit number)

13130627512104776627…14963831234886214399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.313 × 10⁹⁶(97-digit number)

13130627512104776627…14963831234886214401

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

2.626 × 10⁹⁶(97-digit number)

26261255024209553255…29927662469772428799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.626 × 10⁹⁶(97-digit number)

26261255024209553255…29927662469772428801

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

5.252 × 10⁹⁶(97-digit number)

52522510048419106510…59855324939544857599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.252 × 10⁹⁶(97-digit number)

52522510048419106510…59855324939544857601

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

1.050 × 10⁹⁷(98-digit number)

10504502009683821302…19710649879089715199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.050 × 10⁹⁷(98-digit number)

10504502009683821302…19710649879089715201

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 #2,083,927

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