Block #2,155,676

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/11/2017, 3:13:09 AM · Difficulty 10.9058 · 4,686,650 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0a3991889b4afd1def1897a7a47449aa6e55f092613cbfbd76bb2d47a8fe5d9

View on Chainz ↗

Height

#2,155,676

Difficulty

10.905822

Transactions

Size

2.64 KB

Version

Bits

0ae7e3fa

Nonce

560,400,450

Timestamp

6/11/2017, 3:13:09 AM

Confirmations

4,686,650

Mined by

⛏️ P2SHAY43mBZESrTRC8xrKNNWJv5e9DbQajJkDy

Merkle Root

892df382eb736b169ebf38c76ead2d3d3c4c715b0e13903f5f5b86e76798f542

Transactions (5)

Coinbase07b665ca76319a…a8a4911a061d6a

1 in → 1 out8.4400 XPM110 B

AY43mBZE…bQajJkDy

6530c0e4b72bd0…83b71580e3049e

7 in → 2 out1135.2450 XPM1.09 KB

ASUH7WPo…WvKxcxei ANZz6eJN…M2qZH2sq

f6ab0907251513…f0a2cc5812887c

1 in → 2 out8.3900 XPM192 B

ASdXKexa…kch59HW5 AUCFrTgV…nXHwXC4W

79309afe417461…25f67d59812e0f

2 in → 2 out21.3816 XPM375 B

AauXdhbL…FTF5E63q ASUP8dmC…hGtzKzFG

6f5a50a462cf4d…81cea5cce8e670

5 in → 2 out4.1228 XPM817 B

AXqh5gyL…QRZriTjq ANP9Msm5…tnnC3N8T

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.

2.923 × 10⁹⁶(97-digit number)

29236439927448096193…41655209585659048959

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

2.923 × 10⁹⁶(97-digit number)

29236439927448096193…41655209585659048959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.923 × 10⁹⁶(97-digit number)

29236439927448096193…41655209585659048961

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

5.847 × 10⁹⁶(97-digit number)

58472879854896192387…83310419171318097919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.847 × 10⁹⁶(97-digit number)

58472879854896192387…83310419171318097921

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

1.169 × 10⁹⁷(98-digit number)

11694575970979238477…66620838342636195839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.169 × 10⁹⁷(98-digit number)

11694575970979238477…66620838342636195841

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

2.338 × 10⁹⁷(98-digit number)

23389151941958476954…33241676685272391679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.338 × 10⁹⁷(98-digit number)

23389151941958476954…33241676685272391681

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

4.677 × 10⁹⁷(98-digit number)

46778303883916953909…66483353370544783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.677 × 10⁹⁷(98-digit number)

46778303883916953909…66483353370544783361

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 #2,155,676

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