Block #537,760

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/12/2014, 1:30:51 AM · Difficulty 10.9169 · 6,258,365 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

18906c85e7196f0680f130ac6b7729f3149de2c851c23574111d983b2e74b688

View on Chainz ↗

Height

#537,760

Difficulty

10.916936

Transactions

Size

4.70 KB

Version

Bits

0aeabc53

Nonce

420,872,398

Timestamp

5/12/2014, 1:30:51 AM

Confirmations

6,258,365

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a140967c55d1999e086b5d5d0e220968904258b4f62883d127ff02dea2eb494e

Transactions (5)

Coinbase41e71649b6ae0a…1328df835696c8

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

797fbec78860bb…9464e58c9f4fb8

5 in → 2 out15.0366 XPM817 B

ANBKo68j…FknjdrB2 AQ1VXrXu…YCH7BDET

8bc7d135b6edfc…a25532dede4491

22 in → 2 out66.5765 XPM3.26 KB

AHmfWGUv…ueCN7GwE AVgq6VwZ…Vthv2GVf

c7e73adac5e0b6…bf8d026b1a21e2

1 in → 2 out6.2618 XPM226 B

AVQWLeav…PiJRU96B AGNi8hqE…G9NxEWHh

d588bd5eb53101…b763e987a755e0

1 in → 2 out0.6196 XPM227 B

APY6bU6F…oQXHVm48 AJ4CzefV…v88s3kBm

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.

8.608 × 10⁹⁹(100-digit number)

86088010685206342951…60058145076054803199

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

8.608 × 10⁹⁹(100-digit number)

86088010685206342951…60058145076054803199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.608 × 10⁹⁹(100-digit number)

86088010685206342951…60058145076054803201

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

1.721 × 10¹⁰⁰(101-digit number)

17217602137041268590…20116290152109606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.721 × 10¹⁰⁰(101-digit number)

17217602137041268590…20116290152109606401

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

3.443 × 10¹⁰⁰(101-digit number)

34435204274082537180…40232580304219212799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.443 × 10¹⁰⁰(101-digit number)

34435204274082537180…40232580304219212801

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

6.887 × 10¹⁰⁰(101-digit number)

68870408548165074361…80465160608438425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.887 × 10¹⁰⁰(101-digit number)

68870408548165074361…80465160608438425601

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

1.377 × 10¹⁰¹(102-digit number)

13774081709633014872…60930321216876851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.377 × 10¹⁰¹(102-digit number)

13774081709633014872…60930321216876851201

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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