Block #977,025

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2015, 12:33:10 PM · Difficulty 10.8477 · 5,832,877 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3829ac0a052de721f53c0f401309fb01cd1f9a5c5348bc3ae667a81b12373706

View on Chainz ↗

Height

#977,025

Difficulty

10.847723

Transactions

Size

2.41 KB

Version

Bits

0ad9045b

Nonce

1,887,000,560

Timestamp

3/16/2015, 12:33:10 PM

Confirmations

5,832,877

Mined by

⛏️ P2SHARGGvuCnq3DJ9E1RyKhGD6p88r6Z35KcGy

Merkle Root

f8858fc4f3d720ad138b9048593028fe791e8870665f6a0faa0afe287bce1bd7

Transactions (3)

Coinbase0b97431aa0b99d…d207938e714909

1 in → 1 out8.5100 XPM109 B

ARGGvuCn…6Z35KcGy

07e730ab42494e…f62b04dc5faedc

1 in → 51 out31.4272 XPM1.85 KB

APM3RoGj…Vb6frVuB AcAYXubV…72sadqng ASXHTHpX…WDAnxNxJ AS8tXSFT…PVqdRMGe ARuuBU5X…TBLN4MWx

9504adc67dcf59…b582acc8c38c18

2 in → 2 out5.1134 XPM375 B

AcKerPva…qeeuPChG AH89E6UM…vhjyLkvP

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.

6.412 × 10⁹⁵(96-digit number)

64126419002582279543…06699364600079891199

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

6.412 × 10⁹⁵(96-digit number)

64126419002582279543…06699364600079891199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.412 × 10⁹⁵(96-digit number)

64126419002582279543…06699364600079891201

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

1.282 × 10⁹⁶(97-digit number)

12825283800516455908…13398729200159782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.282 × 10⁹⁶(97-digit number)

12825283800516455908…13398729200159782401

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

2.565 × 10⁹⁶(97-digit number)

25650567601032911817…26797458400319564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.565 × 10⁹⁶(97-digit number)

25650567601032911817…26797458400319564801

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

5.130 × 10⁹⁶(97-digit number)

51301135202065823634…53594916800639129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.130 × 10⁹⁶(97-digit number)

51301135202065823634…53594916800639129601

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

1.026 × 10⁹⁷(98-digit number)

10260227040413164726…07189833601278259199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.026 × 10⁹⁷(98-digit number)

10260227040413164726…07189833601278259201

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 #977,025

Cookie Preferences