Block #583,264

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/10/2014, 10:42:04 AM · Difficulty 10.9576 · 6,223,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a50baa49755ac3d9b9871bbe67aee05ae2b7e200e6b5c9b949ba656913b0b555

View on Chainz ↗

Height

#583,264

Difficulty

10.957584

Transactions

Size

993 B

Version

Bits

0af5243b

Nonce

586,999

Timestamp

6/10/2014, 10:42:04 AM

Confirmations

6,223,512

Mined by

⛏️ `aSAJzWx2VDShfKP9pKK3jZqTbn4sj4ZSMit5

Merkle Root

18661b27458ad0fbb6f85f5a5cb187d5697e45ba5a4ba8f405b58697686c425f

Transactions (2)

Coinbased1256955c82949…7c5907af649732

1 in → 18 out8.3200 XPM675 B

AJzWx2VD…j4ZSMit5 AQv2iMwd…EFna22ee AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn AQwRN8bE…V8PsTcY9

ab5e50fc8aadac…dd587c2534dd61

1 in → 2 out8.2900 XPM226 B

AcuVf6G2…Hb6Kfkoa AGpvdZiL…yRF55qor

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.

4.896 × 10¹⁰⁰(101-digit number)

48964431437426318783…23867597902663720999

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

4.896 × 10¹⁰⁰(101-digit number)

48964431437426318783…23867597902663720999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.896 × 10¹⁰⁰(101-digit number)

48964431437426318783…23867597902663721001

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

9.792 × 10¹⁰⁰(101-digit number)

97928862874852637567…47735195805327441999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.792 × 10¹⁰⁰(101-digit number)

97928862874852637567…47735195805327442001

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

1.958 × 10¹⁰¹(102-digit number)

19585772574970527513…95470391610654883999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.958 × 10¹⁰¹(102-digit number)

19585772574970527513…95470391610654884001

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

3.917 × 10¹⁰¹(102-digit number)

39171545149941055027…90940783221309767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.917 × 10¹⁰¹(102-digit number)

39171545149941055027…90940783221309768001

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

7.834 × 10¹⁰¹(102-digit number)

78343090299882110054…81881566442619535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.834 × 10¹⁰¹(102-digit number)

78343090299882110054…81881566442619536001

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

1.566 × 10¹⁰²(103-digit number)

15668618059976422010…63763132885239071999

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 #583,264

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