Block #537,882

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/12/2014, 2:45:54 AM · Difficulty 10.9177 · 6,289,003 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9c79a80fc89d34a25e4379cd92a23f0cf1c9ecf90f15ec077446a33474d5f9e

View on Chainz ↗

Height

#537,882

Difficulty

10.917709

Transactions

Size

4.73 KB

Version

Bits

0aeaeeff

Nonce

155,282,977

Timestamp

5/12/2014, 2:45:54 AM

Confirmations

6,289,003

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

14e7f7c6ccb342fb49cea2398a594a2591cd3c9bbd41753f0ea1daffdb179a74

Transactions (5)

Coinbase85d44511c2e992…bf1e40d40c4411

1 in → 1 out8.4700 XPM116 B

ANSXnLY2…Sd25TjkD

6dc4ac207171ab…9b498164615b4b

25 in → 2 out500.0100 XPM3.69 KB

AJjnK9uC…VreFquR4 AVjFu3V7…MLT7cwJx

60a30847ca9ec3…9c9b42956797db

2 in → 3 out6.2873 XPM408 B

ANxzqMDP…VsNAPahg AWppzrSM…CxCJ4whA AeKNrjNj…1NEq95Ta

6bad0f13112087…95ea95d15857d1

1 in → 2 out3.0676 XPM225 B

AGoKcyWu…JUGdp2ZN AMAxLjXk…843iHH6r

7a6cedcd23d5c7…085393a420776c

1 in → 2 out1.4621 XPM227 B

ARiDyh5W…MyYEQ4NS ANCY3LAQ…VVUAaU8Y

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.

5.952 × 10⁹⁹(100-digit number)

59528794769420735706…23476116910388930559

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

5.952 × 10⁹⁹(100-digit number)

59528794769420735706…23476116910388930559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.952 × 10⁹⁹(100-digit number)

59528794769420735706…23476116910388930561

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

1.190 × 10¹⁰⁰(101-digit number)

11905758953884147141…46952233820777861119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.190 × 10¹⁰⁰(101-digit number)

11905758953884147141…46952233820777861121

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

2.381 × 10¹⁰⁰(101-digit number)

23811517907768294282…93904467641555722239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.381 × 10¹⁰⁰(101-digit number)

23811517907768294282…93904467641555722241

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

4.762 × 10¹⁰⁰(101-digit number)

47623035815536588565…87808935283111444479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.762 × 10¹⁰⁰(101-digit number)

47623035815536588565…87808935283111444481

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

9.524 × 10¹⁰⁰(101-digit number)

95246071631073177130…75617870566222888959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.524 × 10¹⁰⁰(101-digit number)

95246071631073177130…75617870566222888961

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

Block #537,882

Cookie Preferences