Block #228,555

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/26/2013, 2:27:15 PM · Difficulty 9.9378 · 6,585,657 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c3aca373241de9f7ddde740f2096536d205e9192f1b4ebcc26debf1a7a07b9a

View on Chainz ↗

Height

#228,555

Difficulty

9.937826

Transactions

Size

2.52 KB

Version

Bits

09f01558

Nonce

206,562

Timestamp

10/26/2013, 2:27:15 PM

Confirmations

6,585,657

Mined by

⛏️ P2SHAe4w1GUtLBhEQ1CmsMEsqByfyQ7BMBvhP2

Merkle Root

ff43844f58305a56f8e1030fe31f3ff61ab7a71d7a47824a34836f83d50b1722

Transactions (5)

Coinbase41038aa491fb29…a9154052b98091

1 in → 1 out10.1600 XPM109 B

Ae4w1GUt…7BMBvhP2

3aa18e0104597f…5fe0437b24dfcb

3 in → 2 out7.1219 XPM523 B

ANThwWTs…H7ZfDQZC AVYNF26Q…rY1vxyQj

970b571b605d05…a20f33beea26fe

8 in → 2 out32.2998 XPM1.23 KB

AQexqQM9…48P1kXWc ANr83vDy…9uqn5ymx

5efd35bb071e5e…539122d9f4cab7

1 in → 2 out3.0659 XPM226 B

AYYa36ng…Lqhe2f76 ATtkfa6o…2cnR55io

74ba68f8fa1ba4…d3ed36c36a9cf8

2 in → 2 out2.1272 XPM373 B

AHS2pvih…hRzcD59k APXier5M…Wixf6QtC

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.

8.789 × 10⁹²(93-digit number)

87896886991081684500…24972896938020681419

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

8.789 × 10⁹²(93-digit number)

87896886991081684500…24972896938020681419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.789 × 10⁹²(93-digit number)

87896886991081684500…24972896938020681421

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

1.757 × 10⁹³(94-digit number)

17579377398216336900…49945793876041362839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.757 × 10⁹³(94-digit number)

17579377398216336900…49945793876041362841

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

3.515 × 10⁹³(94-digit number)

35158754796432673800…99891587752082725679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.515 × 10⁹³(94-digit number)

35158754796432673800…99891587752082725681

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

7.031 × 10⁹³(94-digit number)

70317509592865347600…99783175504165451359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.031 × 10⁹³(94-digit number)

70317509592865347600…99783175504165451361

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

1.406 × 10⁹⁴(95-digit number)

14063501918573069520…99566351008330902719

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 #228,555

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