Block #2,136,505

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/29/2017, 5:16:48 AM · Difficulty 10.8939 · 4,709,198 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e43c41be18012f8be0f4643363b2d5df45f0e0a91d590c6f682df4eb39a84002

View on Chainz ↗

Height

#2,136,505

Difficulty

10.893943

Transactions

Size

2.44 KB

Version

Bits

0ae4d973

Nonce

1,711,240,340

Timestamp

5/29/2017, 5:16:48 AM

Confirmations

4,709,198

Mined by

⛏️ P2SHAaHSyqQp72zb3SavfETL2XfhZt5U42SCBS

Merkle Root

386d6462385e0f18bbcaa2640957fbf51aa08aa3a744f807214cd7a7e11fe470

Transactions (4)

Coinbasede9264a859c638…943fd14c5a5589

1 in → 1 out8.4500 XPM109 B

AaHSyqQp…5U42SCBS

f639f2ec90c532…cd94523763954c

8 in → 2 out1629.0553 XPM1.23 KB

APaUJKaq…4f9TQWYR AGDjnHo6…BEseJKBT

ee35ac2dc9f0c7…7c05a4ba23c1d7

1 in → 2 out6.6573 XPM226 B

AWuKWtqq…wsByBjYh ANCGVTkJ…8AP3sQiR

54d8493e1814fe…49bccd9b5a91b6

5 in → 2 out1.0482 XPM816 B

ANwtSRNc…za9KnLoD AYtybcAs…2URCMbGn

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.

1.290 × 10⁹⁵(96-digit number)

12908419564478649561…84443511062994329599

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

1.290 × 10⁹⁵(96-digit number)

12908419564478649561…84443511062994329599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.290 × 10⁹⁵(96-digit number)

12908419564478649561…84443511062994329601

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

2.581 × 10⁹⁵(96-digit number)

25816839128957299123…68887022125988659199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.581 × 10⁹⁵(96-digit number)

25816839128957299123…68887022125988659201

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

5.163 × 10⁹⁵(96-digit number)

51633678257914598246…37774044251977318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.163 × 10⁹⁵(96-digit number)

51633678257914598246…37774044251977318401

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

1.032 × 10⁹⁶(97-digit number)

10326735651582919649…75548088503954636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.032 × 10⁹⁶(97-digit number)

10326735651582919649…75548088503954636801

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

2.065 × 10⁹⁶(97-digit number)

20653471303165839298…51096177007909273599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.065 × 10⁹⁶(97-digit number)

20653471303165839298…51096177007909273601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.130 × 10⁹⁶(97-digit number)

41306942606331678596…02192354015818547199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,136,505

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