Block #591,772

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/17/2014, 7:56:51 AM · Difficulty 10.9442 · 6,211,991 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c3265b2bfa03cdfd0616a3ffb381002e356922377ecf31efb4d8bb7378d0122

View on Chainz ↗

Height

#591,772

Difficulty

10.944207

Transactions

Size

1.01 KB

Version

Bits

0af1b787

Nonce

277,006,771

Timestamp

6/17/2014, 7:56:51 AM

Confirmations

6,211,991

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7bf9edde0f0f91d1a867ac51e69273b9d0e6a7b7b52f35a1b5e2e08ee304478b

Transactions (4)

Coinbasefe7615b1f40e14…fa00b4a235f418

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

6f3e523526717f…2bd655a34d3036

2 in → 2 out28.4264 XPM372 B

AQfYd8c6…32CSHhsY AR3NsN6L…zoMC9e95

9749644250c598…f1cdcd2a6ee53a

1 in → 2 out6.0401 XPM226 B

AKBp1zZ5…q1DHcgUx AVkK3Rcq…ifLMN9nx

859f9e851a27d3…162ab9c43c9cb8

1 in → 2 out2.0147 XPM226 B

Ae7YXEyn…hnSYZsCr AL33pZ4R…5jQJ63us

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.

5.949 × 10¹⁰⁰(101-digit number)

59490686775252719455…46882021724389375999

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

5.949 × 10¹⁰⁰(101-digit number)

59490686775252719455…46882021724389375999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.949 × 10¹⁰⁰(101-digit number)

59490686775252719455…46882021724389376001

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

1.189 × 10¹⁰¹(102-digit number)

11898137355050543891…93764043448778751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.189 × 10¹⁰¹(102-digit number)

11898137355050543891…93764043448778752001

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

2.379 × 10¹⁰¹(102-digit number)

23796274710101087782…87528086897557503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.379 × 10¹⁰¹(102-digit number)

23796274710101087782…87528086897557504001

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

4.759 × 10¹⁰¹(102-digit number)

47592549420202175564…75056173795115007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.759 × 10¹⁰¹(102-digit number)

47592549420202175564…75056173795115008001

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

9.518 × 10¹⁰¹(102-digit number)

95185098840404351128…50112347590230015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.518 × 10¹⁰¹(102-digit number)

95185098840404351128…50112347590230016001

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

1.903 × 10¹⁰²(103-digit number)

19037019768080870225…00224695180460031999

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