Block #84,981

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 4:08:41 AM · Difficulty 9.2806 · 6,709,535 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26328a01e504e3f78360db928e2ebb737bad115812b5bbe190f162ddc194d862

View on Chainz ↗

Height

#84,981

Difficulty

9.280615

Transactions

Size

206 B

Version

Bits

0947d65c

Nonce

52,646

Timestamp

7/27/2013, 4:08:41 AM

Confirmations

6,709,535

Mined by

⛏️ P2SHANG6Vi1KaioxzUkKHHVZMpkj9tywYbtuVR

Merkle Root

577eec4cc3e88e30fc89f39b93381eeb8a47e2023450189a1204218343eded0d

Transactions (1)

Coinbase577eec4cc3e88e…04218343eded0d

1 in → 1 out11.5900 XPM109 B

ANG6Vi1K…ywYbtuVR

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 × 10¹¹⁰(111-digit number)

18173462314021199945…51784848098577744369

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 × 10¹¹⁰(111-digit number)

18173462314021199945…51784848098577744369

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.817 × 10¹¹⁰(111-digit number)

18173462314021199945…51784848098577744371

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

3.634 × 10¹¹⁰(111-digit number)

36346924628042399891…03569696197155488739

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.634 × 10¹¹⁰(111-digit number)

36346924628042399891…03569696197155488741

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

7.269 × 10¹¹⁰(111-digit number)

72693849256084799783…07139392394310977479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.269 × 10¹¹⁰(111-digit number)

72693849256084799783…07139392394310977481

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

1.453 × 10¹¹¹(112-digit number)

14538769851216959956…14278784788621954959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.453 × 10¹¹¹(112-digit number)

14538769851216959956…14278784788621954961

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

2.907 × 10¹¹¹(112-digit number)

29077539702433919913…28557569577243909919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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