Block #2,128,837

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2017, 5:25:58 AM · Difficulty 10.9121 · 4,713,350 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fb46d526089409f19b79cbbfc0cad51161fddc300635562cc01d1072cbc7a2ed

View on Chainz ↗

Height

#2,128,837

Difficulty

10.912110

Transactions

Size

1.14 KB

Version

Bits

0ae98005

Nonce

558,585,919

Timestamp

5/23/2017, 5:25:58 AM

Confirmations

4,713,350

Mined by

⛏️ P2SHAZd7rsY4ZZQzefSFbNdVZTY8HA4tM5qBPo

Merkle Root

22eb3138a43fde869cff9cb22c506b99df7577163ed7c4f47444b54724d0e9e3

Transactions (4)

Coinbaseef25c42b3401f2…be0a97620073f9

1 in → 1 out8.4100 XPM109 B

AZd7rsY4…4tM5qBPo

3137f4fbbad066…efb21a43b71a7c

1 in → 2 out520.7903 XPM226 B

AV87tPG9…qykkkkao AWwKXxET…gabHVYya

466dda3c5e5aa7…dee2e78f9a94d8

1 in → 2 out487.2838 XPM226 B

AeG8VpJd…1k9UoGZc AUjQrkhm…khbAaW2W

f84d8bea82dd52…b76223dcc1caa7

3 in → 2 out221.8791 XPM520 B

AaEkL9U2…HFNsh9fa AZJ1uFRS…B7nQLknD

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.

1.222 × 10⁹⁴(95-digit number)

12226762169374225855…16051602288627579599

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

1.222 × 10⁹⁴(95-digit number)

12226762169374225855…16051602288627579599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.222 × 10⁹⁴(95-digit number)

12226762169374225855…16051602288627579601

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

2.445 × 10⁹⁴(95-digit number)

24453524338748451710…32103204577255159199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.445 × 10⁹⁴(95-digit number)

24453524338748451710…32103204577255159201

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

4.890 × 10⁹⁴(95-digit number)

48907048677496903420…64206409154510318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.890 × 10⁹⁴(95-digit number)

48907048677496903420…64206409154510318401

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

9.781 × 10⁹⁴(95-digit number)

97814097354993806840…28412818309020636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.781 × 10⁹⁴(95-digit number)

97814097354993806840…28412818309020636801

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

1.956 × 10⁹⁵(96-digit number)

19562819470998761368…56825636618041273599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.956 × 10⁹⁵(96-digit number)

19562819470998761368…56825636618041273601

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 #2,128,837

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