Block #2,376,279

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/12/2017, 12:20:36 PM · Difficulty 10.8813 · 4,467,346 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bd3cb535ac323548a45485e74d786b95c918a2b5c4a9f1e9d6b0cd3a9d0bd0de

View on Chainz ↗

Height

#2,376,279

Difficulty

10.881311

Transactions

Size

944 B

Version

Bits

0ae19d95

Nonce

1,574,175,550

Timestamp

11/12/2017, 12:20:36 PM

Confirmations

4,467,346

Mined by

⛏️ P2SHAKseBdvCfS8MJHNaMSRao83oyaA1BxneCt

Merkle Root

38d6fbd3d9378224c6fc5be048fb14a5d31fd1f05df2beb776f7b8d8313d692a

Transactions (3)

Coinbasece9e53808da301…d8e4b2278ff445

1 in → 1 out8.4500 XPM109 B

AKseBdvC…A1BxneCt

194ce9c25dcb01…476f099269c830

1 in → 2 out6.3449 XPM226 B

AKatK3j1…WGrp4VZL AVKQEWvC…C6k5sVTJ

2006fc52d14bcd…27801db0303409

3 in → 2 out4.4599 XPM520 B

AJDuWfPK…nypbGzCV AJMrMUVA…XLVBXChy

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.

2.386 × 10⁹³(94-digit number)

23860587367252347512…78252520540638077439

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

2.386 × 10⁹³(94-digit number)

23860587367252347512…78252520540638077439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.386 × 10⁹³(94-digit number)

23860587367252347512…78252520540638077441

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

4.772 × 10⁹³(94-digit number)

47721174734504695025…56505041081276154879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.772 × 10⁹³(94-digit number)

47721174734504695025…56505041081276154881

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

9.544 × 10⁹³(94-digit number)

95442349469009390051…13010082162552309759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.544 × 10⁹³(94-digit number)

95442349469009390051…13010082162552309761

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

1.908 × 10⁹⁴(95-digit number)

19088469893801878010…26020164325104619519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.908 × 10⁹⁴(95-digit number)

19088469893801878010…26020164325104619521

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

3.817 × 10⁹⁴(95-digit number)

38176939787603756020…52040328650209239039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.817 × 10⁹⁴(95-digit number)

38176939787603756020…52040328650209239041

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

7.635 × 10⁹⁴(95-digit number)

76353879575207512041…04080657300418478079

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 #2,376,279

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