Block #2,142,108

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/2/2017, 5:16:24 PM · Difficulty 10.8740 · 4,696,767 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

52e7340a8761111c083d6f7297587fae92599d42dce60f0cd99d2a91ae5ee8af

View on Chainz ↗

Height

#2,142,108

Difficulty

10.874000

Transactions

Size

573 B

Version

Bits

0adfbe79

Nonce

678,272,898

Timestamp

6/2/2017, 5:16:24 PM

Confirmations

4,696,767

Mined by

⛏️ P2SHALMfkc2QiW1CV7MvnXf479ibRUefCWTR5r

Merkle Root

cc18f729c2f511cd56aacd59b3f27becd1e090adaddb8b85812b1fc85267d0af

Transactions (2)

Coinbase70f01d353de9ee…e9aa44b251f8b2

1 in → 1 out8.4500 XPM109 B

ALMfkc2Q…efCWTR5r

f45dd33f0bd7e0…95409a35a1e39b

2 in → 2 out861.6870 XPM374 B

AeMFZAjx…UbXPTGfm AM5iAcHi…EaSLASCq

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.

4.923 × 10⁹⁵(96-digit number)

49231120853098388053…48714593495736019199

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

4.923 × 10⁹⁵(96-digit number)

49231120853098388053…48714593495736019199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.923 × 10⁹⁵(96-digit number)

49231120853098388053…48714593495736019201

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

9.846 × 10⁹⁵(96-digit number)

98462241706196776106…97429186991472038399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.846 × 10⁹⁵(96-digit number)

98462241706196776106…97429186991472038401

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

1.969 × 10⁹⁶(97-digit number)

19692448341239355221…94858373982944076799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.969 × 10⁹⁶(97-digit number)

19692448341239355221…94858373982944076801

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

3.938 × 10⁹⁶(97-digit number)

39384896682478710442…89716747965888153599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.938 × 10⁹⁶(97-digit number)

39384896682478710442…89716747965888153601

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

7.876 × 10⁹⁶(97-digit number)

78769793364957420885…79433495931776307199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.876 × 10⁹⁶(97-digit number)

78769793364957420885…79433495931776307201

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 #2,142,108

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