Block #3,002,767

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/10/2019, 12:08:06 AM · Difficulty 11.2015 · 3,839,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1804a71c6ab8fb3869dd85c590619340673e1857844d2196e69c236ed15b6bda

View on Chainz ↗

Height

#3,002,767

Difficulty

11.201455

Transactions

Size

1022 B

Version

Bits

0b339291

Nonce

539,608,525

Timestamp

1/10/2019, 12:08:06 AM

Confirmations

3,839,476

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

b55c0f94e1b638534c7398eff6419e0f1e13c8633595e229798fc0dd14bf0308

Transactions (2)

Coinbasea19140be2ea39d…5e3fb614bb5fdb

1 in → 1 out7.9700 XPM110 B

AUhjokok…k5m93PZR

66f52d46109027…8b016b5b97122e

5 in → 2 out797.0633 XPM821 B

AZUV1W6L…rfiLtPKM Af13GECN…BxUJJfsD

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.

9.905 × 10⁹⁵(96-digit number)

99058454317355133823…13284664556329983999

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

9.905 × 10⁹⁵(96-digit number)

99058454317355133823…13284664556329983999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.905 × 10⁹⁵(96-digit number)

99058454317355133823…13284664556329984001

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

1.981 × 10⁹⁶(97-digit number)

19811690863471026764…26569329112659967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.981 × 10⁹⁶(97-digit number)

19811690863471026764…26569329112659968001

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

3.962 × 10⁹⁶(97-digit number)

39623381726942053529…53138658225319935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.962 × 10⁹⁶(97-digit number)

39623381726942053529…53138658225319936001

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

7.924 × 10⁹⁶(97-digit number)

79246763453884107058…06277316450639871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.924 × 10⁹⁶(97-digit number)

79246763453884107058…06277316450639872001

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

1.584 × 10⁹⁷(98-digit number)

15849352690776821411…12554632901279743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.584 × 10⁹⁷(98-digit number)

15849352690776821411…12554632901279744001

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

3.169 × 10⁹⁷(98-digit number)

31698705381553642823…25109265802559487999

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 #3,002,767

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