Block #2,224,925

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/27/2017, 7:22:35 AM · Difficulty 10.9474 · 4,589,296 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd1960a1d8b95b9a9f3fac2cd2b5a74e170e593bfa590fc52c2f8a85efb5e9d9

View on Chainz ↗

Height

#2,224,925

Difficulty

10.947352

Transactions

Size

1.17 KB

Version

Bits

0af285a3

Nonce

309,859,550

Timestamp

7/27/2017, 7:22:35 AM

Confirmations

4,589,296

Mined by

⛏️ P2SHAJ81EWDSqFW4zSB1Zxq5PnhDMQvjZkridU

Merkle Root

1d4abaab22d97258bed671d9a31dd92b19be85737c1c795479ef5905126c35a5

Transactions (2)

Coinbased54c3c44667eec…42d96191dde574

1 in → 1 out8.3500 XPM110 B

AJ81EWDS…vjZkridU

bf51ec8696ab32…e305b6a4eab9e4

6 in → 3 out769.4663 XPM1001 B

AVN9uRjG…V3ZGnUph Ac9Rrpcw…KXWZpRRE AdLv38Pf…k1z3e6Dc

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.

9.772 × 10⁹³(94-digit number)

97727809557040601590…56123038907953706399

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

9.772 × 10⁹³(94-digit number)

97727809557040601590…56123038907953706399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.772 × 10⁹³(94-digit number)

97727809557040601590…56123038907953706401

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

1.954 × 10⁹⁴(95-digit number)

19545561911408120318…12246077815907412799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.954 × 10⁹⁴(95-digit number)

19545561911408120318…12246077815907412801

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

3.909 × 10⁹⁴(95-digit number)

39091123822816240636…24492155631814825599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.909 × 10⁹⁴(95-digit number)

39091123822816240636…24492155631814825601

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

7.818 × 10⁹⁴(95-digit number)

78182247645632481272…48984311263629651199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.818 × 10⁹⁴(95-digit number)

78182247645632481272…48984311263629651201

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

1.563 × 10⁹⁵(96-digit number)

15636449529126496254…97968622527259302399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.563 × 10⁹⁵(96-digit number)

15636449529126496254…97968622527259302401

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

3.127 × 10⁹⁵(96-digit number)

31272899058252992508…95937245054518604799

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 #2,224,925

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