Block #1,179,220

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/1/2015, 8:18:20 AM · Difficulty 10.9311 · 5,624,163 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e889361734ade2bbe0b66f347755b749413bd1bf9b559af111410b2d48e20d9

View on Chainz ↗

Height

#1,179,220

Difficulty

10.931074

Transactions

Size

90.25 KB

Version

Bits

0aee5ae3

Nonce

712,818,469

Timestamp

8/1/2015, 8:18:20 AM

Confirmations

5,624,163

Mined by

⛏️ P2SHAdsA6pLWkUSZfWF1rvtnwQ6fu5yuhgH1Tv

Merkle Root

d76645287e3a6b3184a8b6f7475e7c7f70961ef5840b634ff7faad0d6e086b38

Transactions (3)

Coinbaseb04c500243ed40…c1a4da66a4b5b7

1 in → 1 out9.3000 XPM109 B

AdsA6pLW…yuhgH1Tv

d7548cf412abe8…54685fef8800de

615 in → 2 out200.0100 XPM88.97 KB

Aej4QUCz…SVr9QNE3 AYmJwjcE…JuBUL1Xc

75d492331855ee…db7f2c262d6bda

7 in → 2 out7.0720 XPM1.08 KB

AJHP38YZ…qUrAD3kn AJVr27wk…5W7xgWAq

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.

1.817 × 10⁹⁷(98-digit number)

18179562830043656747…45517775840365363199

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

1.817 × 10⁹⁷(98-digit number)

18179562830043656747…45517775840365363199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.817 × 10⁹⁷(98-digit number)

18179562830043656747…45517775840365363201

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

3.635 × 10⁹⁷(98-digit number)

36359125660087313494…91035551680730726399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.635 × 10⁹⁷(98-digit number)

36359125660087313494…91035551680730726401

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

7.271 × 10⁹⁷(98-digit number)

72718251320174626989…82071103361461452799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.271 × 10⁹⁷(98-digit number)

72718251320174626989…82071103361461452801

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

1.454 × 10⁹⁸(99-digit number)

14543650264034925397…64142206722922905599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.454 × 10⁹⁸(99-digit number)

14543650264034925397…64142206722922905601

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

2.908 × 10⁹⁸(99-digit number)

29087300528069850795…28284413445845811199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.908 × 10⁹⁸(99-digit number)

29087300528069850795…28284413445845811201

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