Block #1,223,326

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/5/2015, 3:27:39 PM · Difficulty 10.7408 · 5,592,592 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83057300846cf43c071b0ea86c62e785430fbc74b8008af473c43fe6ab7f3743

View on Chainz ↗

Height

#1,223,326

Difficulty

10.740799

Transactions

Size

10.55 KB

Version

Bits

0abda4ff

Nonce

293,293,401

Timestamp

9/5/2015, 3:27:39 PM

Confirmations

5,592,592

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

7502f1980e882f83e1332191e9a3307d3d7adff214251277f2424164f5416e4b

Transactions (4)

Coinbasea91fc274eaedb2…cf2d5c468f0c82

1 in → 1 out8.7800 XPM116 B

AJCEY9yy…tg97E6zm

9f92b599195e1a…2dffc93c14ff24

68 in → 2 out500.0100 XPM9.91 KB

AYpTebZm…WDuXg1sV AJjnK9uC…VreFquR4

d9254e87764c98…db160848b6f8b4

1 in → 2 out6.5361 XPM226 B

AXoDQNbV…s3BWmXji AcuM7XiJ…5uND8Jce

83124e9ede850d…cf8fe231810c5d

1 in → 2 out0.6236 XPM226 B

AK2CsaKQ…PjQuNdUB AWjkfEsZ…YmqM8aM7

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.

3.066 × 10⁹⁷(98-digit number)

30669567965727795753…29512283927226918399

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

3.066 × 10⁹⁷(98-digit number)

30669567965727795753…29512283927226918399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.066 × 10⁹⁷(98-digit number)

30669567965727795753…29512283927226918401

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

6.133 × 10⁹⁷(98-digit number)

61339135931455591506…59024567854453836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.133 × 10⁹⁷(98-digit number)

61339135931455591506…59024567854453836801

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

1.226 × 10⁹⁸(99-digit number)

12267827186291118301…18049135708907673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.226 × 10⁹⁸(99-digit number)

12267827186291118301…18049135708907673601

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

2.453 × 10⁹⁸(99-digit number)

24535654372582236602…36098271417815347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.453 × 10⁹⁸(99-digit number)

24535654372582236602…36098271417815347201

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

4.907 × 10⁹⁸(99-digit number)

49071308745164473204…72196542835630694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.907 × 10⁹⁸(99-digit number)

49071308745164473204…72196542835630694401

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 #1,223,326

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