Block #2,268,404

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/26/2017, 5:45:12 AM · Difficulty 10.9524 · 4,557,778 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33db0a7f03d971382f2a9c82c97494dc7f5bb5f4d9a2ba4e8c570b2c59d989d0

View on Chainz ↗

Height

#2,268,404

Difficulty

10.952375

Transactions

Size

1.28 KB

Version

Bits

0af3cedb

Nonce

701,747,647

Timestamp

8/26/2017, 5:45:12 AM

Confirmations

4,557,778

Mined by

⛏️ P2SHAcxgCcumq6jQv7UTfzrgXDzRoJwCgSdcss

Merkle Root

1a052ce29e10d36b02568c3ff51daedfd1d5d5f75970d78d9e668215dc979e84

Transactions (2)

Coinbasede5ab38556dba2…d736557e3d2a2c

1 in → 1 out8.3400 XPM110 B

AcxgCcum…wCgSdcss

8753e70ccde87d…62fcb15f857ae4

7 in → 2 out373.1696 XPM1.09 KB

Ac4cHzMh…fe4E7PVo AWVBJzri…1sMkuo1y

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.

2.514 × 10⁹⁸(99-digit number)

25141223862534861741…20794154483464601599

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

2.514 × 10⁹⁸(99-digit number)

25141223862534861741…20794154483464601599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.514 × 10⁹⁸(99-digit number)

25141223862534861741…20794154483464601601

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

5.028 × 10⁹⁸(99-digit number)

50282447725069723482…41588308966929203199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.028 × 10⁹⁸(99-digit number)

50282447725069723482…41588308966929203201

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

1.005 × 10⁹⁹(100-digit number)

10056489545013944696…83176617933858406399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.005 × 10⁹⁹(100-digit number)

10056489545013944696…83176617933858406401

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

2.011 × 10⁹⁹(100-digit number)

20112979090027889392…66353235867716812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.011 × 10⁹⁹(100-digit number)

20112979090027889392…66353235867716812801

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

4.022 × 10⁹⁹(100-digit number)

40225958180055778785…32706471735433625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.022 × 10⁹⁹(100-digit number)

40225958180055778785…32706471735433625601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.045 × 10⁹⁹(100-digit number)

80451916360111557571…65412943470867251199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,268,404

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