Block #21,059

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 1:30:54 PM · Difficulty 7.9400 · 6,805,930 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

87bff6f7f1b35c5646b80c1bdd9f36b1d448869c53bdff986b6a014f2d670d52

View on Chainz ↗

Height

#21,059

Difficulty

7.939978

Transactions

Size

197 B

Version

Bits

07f0a26b

Nonce

123

Timestamp

7/12/2013, 1:30:54 PM

Confirmations

6,805,930

Mined by

⛏️ P2SHAMD88WR9uHG5EGxCCpAkcCRBhfZhWoLU4a

Merkle Root

0929073eb9fdc97846b58bc122436e255797d67fb216f72859987491b880fb87

Transactions (1)

Coinbase0929073eb9fdc9…987491b880fb87

1 in → 1 out15.8400 XPM108 B

AMD88WR9…ZhWoLU4a

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.

3.391 × 10⁹¹(92-digit number)

33912880195232889546…49896625289277722309

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

3.391 × 10⁹¹(92-digit number)

33912880195232889546…49896625289277722309

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.391 × 10⁹¹(92-digit number)

33912880195232889546…49896625289277722311

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

6.782 × 10⁹¹(92-digit number)

67825760390465779093…99793250578555444619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.782 × 10⁹¹(92-digit number)

67825760390465779093…99793250578555444621

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

1.356 × 10⁹²(93-digit number)

13565152078093155818…99586501157110889239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.356 × 10⁹²(93-digit number)

13565152078093155818…99586501157110889241

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

2.713 × 10⁹²(93-digit number)

27130304156186311637…99173002314221778479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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

Block #21,059

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