Block #2,133,272

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/26/2017, 9:36:50 AM · Difficulty 10.9099 · 4,708,187 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2876dbe83b17189457cf17e982779778e1fddcc5ce6e6416d0d7adb7690f5410

View on Chainz ↗

Height

#2,133,272

Difficulty

10.909862

Transactions

Size

1.74 KB

Version

Bits

0ae8ecbe

Nonce

143,895,577

Timestamp

5/26/2017, 9:36:50 AM

Confirmations

4,708,187

Mined by

⛏️ P2SHAeekuhnjekEAMEJLtWf4jhGwCSPFXnW6jv

Merkle Root

b868a3d870a4bf2d3f38c5369dd1a3d014bd61a5cc1934059a8aaec59f06a9d6

Transactions (3)

Coinbaseebbe72782d833f…8dc3060d750d2f

1 in → 1 out8.4100 XPM109 B

Aeekuhnj…PFXnW6jv

089de0d8a06d64…0bcf8aa82a253a

4 in → 2 out2000.0672 XPM669 B

ARaNCeSx…b8M3uhxY AaTw8zxB…9kwiYjjJ

0294adfacc6565…29be84ab5a65a5

7 in → 2 out52.5659 XPM910 B

AdQVyW6h…woPp73cj AP361J79…sEBNBWjc

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.

3.470 × 10⁹⁶(97-digit number)

34706859026118788449…80523028758139699199

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

3.470 × 10⁹⁶(97-digit number)

34706859026118788449…80523028758139699199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.470 × 10⁹⁶(97-digit number)

34706859026118788449…80523028758139699201

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

6.941 × 10⁹⁶(97-digit number)

69413718052237576899…61046057516279398399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.941 × 10⁹⁶(97-digit number)

69413718052237576899…61046057516279398401

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

1.388 × 10⁹⁷(98-digit number)

13882743610447515379…22092115032558796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.388 × 10⁹⁷(98-digit number)

13882743610447515379…22092115032558796801

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

2.776 × 10⁹⁷(98-digit number)

27765487220895030759…44184230065117593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.776 × 10⁹⁷(98-digit number)

27765487220895030759…44184230065117593601

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

5.553 × 10⁹⁷(98-digit number)

55530974441790061519…88368460130235187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.553 × 10⁹⁷(98-digit number)

55530974441790061519…88368460130235187201

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

1.110 × 10⁹⁸(99-digit number)

11106194888358012303…76736920260470374399

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 #2,133,272

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