Block #228,513

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/26/2013, 1:43:23 PM · Difficulty 9.9379 · 6,575,118 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7ce582d89412761f513bd35d7c9ba979b11b673a22ef219f3e5cc5108adef57

View on Chainz ↗

Height

#228,513

Difficulty

9.937851

Transactions

Size

1.40 KB

Version

Bits

09f01707

Nonce

443,753

Timestamp

10/26/2013, 1:43:23 PM

Confirmations

6,575,118

Mined by

⛏️ |RkAaWqCG7Ns4nMuC4f9u7r3ne5JMdKcG2SFS

Merkle Root

9ca8518170e6acc43e08fd932e5d2752f155d116f4fac1679b36ff50735ae46c

Transactions (2)

Coinbase29191be2d0ad18…3ee40ca10c319a

1 in → 31 out10.0900 XPM1.09 KB

AaWqCG7N…dKcG2SFS AFqKfjez…qX9Ace3g AWCfnjpk…hb1ovL8F AFq51nP4…FqYfXapg Aaox8Rxx…XTyyJXVx

6236217c028645…2cec44a1dd64e4

1 in → 2 out10.1000 XPM226 B

ALWw5pne…DsdpGzi5 AT6mJtaV…LRsGtkk5

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.

7.442 × 10⁸⁹(90-digit number)

74428239879953978091…51999882002651297929

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

7.442 × 10⁸⁹(90-digit number)

74428239879953978091…51999882002651297929

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.442 × 10⁸⁹(90-digit number)

74428239879953978091…51999882002651297931

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

1.488 × 10⁹⁰(91-digit number)

14885647975990795618…03999764005302595859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.488 × 10⁹⁰(91-digit number)

14885647975990795618…03999764005302595861

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

2.977 × 10⁹⁰(91-digit number)

29771295951981591236…07999528010605191719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.977 × 10⁹⁰(91-digit number)

29771295951981591236…07999528010605191721

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

5.954 × 10⁹⁰(91-digit number)

59542591903963182473…15999056021210383439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.954 × 10⁹⁰(91-digit number)

59542591903963182473…15999056021210383441

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

1.190 × 10⁹¹(92-digit number)

11908518380792636494…31998112042420766879

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