Block #1,312,369

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/4/2015, 1:35:43 PM · Difficulty 10.8523 · 5,527,085 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

177d5491b6b3d7884183d1046ace8fff81ed2267d1fe9347871c5a9932a0c00d

View on Chainz ↗

Height

#1,312,369

Difficulty

10.852339

Transactions

Size

1.83 KB

Version

Bits

0ada32df

Nonce

1,299,269,602

Timestamp

11/4/2015, 1:35:43 PM

Confirmations

5,527,085

Mined by

⛏️ P2SHAcivY1QTgBgvZ1eDkJVbQdav9cPPB9HCEB

Merkle Root

51bf58064a3ee431bcb610c6dbfe76e0b74ccc01287b3d5b13ca13ba19e9b274

Transactions (2)

Coinbase234ac8bda425da…d93dd22301f164

1 in → 1 out8.5064 XPM110 B

AcivY1QT…PPB9HCEB

656fb46eedc426…343b979fe3bfee

11 in → 1 out0.2700 XPM1.63 KB

AaVpwrwj…kdqCbURV

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.

2.486 × 10⁹⁸(99-digit number)

24864464970299590455…90489507133373153279

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

2.486 × 10⁹⁸(99-digit number)

24864464970299590455…90489507133373153279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.486 × 10⁹⁸(99-digit number)

24864464970299590455…90489507133373153281

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

4.972 × 10⁹⁸(99-digit number)

49728929940599180910…80979014266746306559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.972 × 10⁹⁸(99-digit number)

49728929940599180910…80979014266746306561

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

9.945 × 10⁹⁸(99-digit number)

99457859881198361820…61958028533492613119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.945 × 10⁹⁸(99-digit number)

99457859881198361820…61958028533492613121

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

1.989 × 10⁹⁹(100-digit number)

19891571976239672364…23916057066985226239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.989 × 10⁹⁹(100-digit number)

19891571976239672364…23916057066985226241

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

3.978 × 10⁹⁹(100-digit number)

39783143952479344728…47832114133970452479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.978 × 10⁹⁹(100-digit number)

39783143952479344728…47832114133970452481

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

7.956 × 10⁹⁹(100-digit number)

79566287904958689456…95664228267940904959

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 #1,312,369

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