Block #217,783

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/19/2013, 1:35:21 PM · Difficulty 9.9288 · 6,591,677 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62f2e0515fff2f4618cc468444512261f5a943d854a1a7a679c70aedd3ff1799

View on Chainz ↗

Height

#217,783

Difficulty

9.928769

Transactions

Size

2.50 KB

Version

Bits

09edc3cf

Nonce

24,540

Timestamp

10/19/2013, 1:35:21 PM

Confirmations

6,591,677

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

87e27b7b1218a7abf7c62d0bfa28f046ee52629b56f73cb360305c76cc3557a0

Transactions (4)

Coinbasee2c1129ecc456e…7a30f118886951

1 in → 1 out10.1700 XPM110 B

AbuU1HhS…JPwsJEbB

c49f69dc279d85…d4f58a33a7abd3

7 in → 2 out691.5462 XPM1.08 KB

AYMuSutZ…AWwDDyo9 AJ2UhagN…75QAaTF6

5dd4f83fa3eac2…e59aed89c8721a

7 in → 2 out61.0361 XPM910 B

Acd1BgN5…bE5c9NoN AcL7E9Uy…Fbq7xuZB

bf3080e6a84587…04e51bcbc439c3

2 in → 1 out1.6589 XPM339 B

AKnYzH4F…AAKwSNmf

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.

6.610 × 10⁹⁴(95-digit number)

66103523404806674133…20516564452238364799

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

6.610 × 10⁹⁴(95-digit number)

66103523404806674133…20516564452238364799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.610 × 10⁹⁴(95-digit number)

66103523404806674133…20516564452238364801

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

1.322 × 10⁹⁵(96-digit number)

13220704680961334826…41033128904476729599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.322 × 10⁹⁵(96-digit number)

13220704680961334826…41033128904476729601

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

2.644 × 10⁹⁵(96-digit number)

26441409361922669653…82066257808953459199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.644 × 10⁹⁵(96-digit number)

26441409361922669653…82066257808953459201

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

5.288 × 10⁹⁵(96-digit number)

52882818723845339306…64132515617906918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.288 × 10⁹⁵(96-digit number)

52882818723845339306…64132515617906918401

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

1.057 × 10⁹⁶(97-digit number)

10576563744769067861…28265031235813836799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #217,783

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