Block #580,459

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/7/2014, 7:31:18 PM · Difficulty 10.9650 · 6,235,575 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65cbf84b5c37b24c5b17e61f78419a26cd37eaca4813c8d7f0d8b258ff81dbb7

View on Chainz ↗

Height

#580,459

Difficulty

10.965009

Transactions

Size

810 B

Version

Bits

0af70ad7

Nonce

147,500,484

Timestamp

6/7/2014, 7:31:18 PM

Confirmations

6,235,575

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8e333111004f8c3fa8c2e6a2c6d43e5b282660bd069351d983f17a9ad58ce077

Transactions (3)

Coinbase509f2277db5da9…28ef94a0fdf58d

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

60b072e5a46b73…30ba75827df1b2

2 in → 2 out16.6100 XPM375 B

AMuz5E94…n1jFU53b ASUbvGQ3…eWcvX9ZX

9dec8e1c216dfd…4c9eecc254dd99

1 in → 2 out8.2900 XPM226 B

AczaAKug…Tyh6SvfG AJVTT67Y…vjUHpcun

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.

1.302 × 10¹⁰²(103-digit number)

13025984069762878040…95630553236491304959

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

1.302 × 10¹⁰²(103-digit number)

13025984069762878040…95630553236491304959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.302 × 10¹⁰²(103-digit number)

13025984069762878040…95630553236491304961

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

2.605 × 10¹⁰²(103-digit number)

26051968139525756081…91261106472982609919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.605 × 10¹⁰²(103-digit number)

26051968139525756081…91261106472982609921

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

5.210 × 10¹⁰²(103-digit number)

52103936279051512163…82522212945965219839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.210 × 10¹⁰²(103-digit number)

52103936279051512163…82522212945965219841

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

1.042 × 10¹⁰³(104-digit number)

10420787255810302432…65044425891930439679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.042 × 10¹⁰³(104-digit number)

10420787255810302432…65044425891930439681

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

2.084 × 10¹⁰³(104-digit number)

20841574511620604865…30088851783860879359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.084 × 10¹⁰³(104-digit number)

20841574511620604865…30088851783860879361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.168 × 10¹⁰³(104-digit number)

41683149023241209730…60177703567721758719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #580,459

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