Block #877,683

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/1/2015, 8:37:49 AM · Difficulty 10.9636 · 5,932,655 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd60e1b43111c77efa046271442ca0ad55362a48c669eddd78f3f6a3518c36af

View on Chainz ↗

Height

#877,683

Difficulty

10.963647

Transactions

Size

878 B

Version

Bits

0af6b196

Nonce

774,020,432

Timestamp

1/1/2015, 8:37:49 AM

Confirmations

5,932,655

Mined by

⛏️ P2SHAHq9YsYapT5i2oH9HxVMEMqSfZqRLKtgrL

Merkle Root

424bc4921d9cbd7f1192c55d7297e28dd26804a218a0791282e1bfa5b808903c

Transactions (4)

Coinbase71b16c34b95dc9…b02518c09a1abc

1 in → 1 out8.3400 XPM110 B

AHq9YsYa…qRLKtgrL

135c95e0110ce2…2cc7484b46c988

1 in → 2 out8.2900 XPM225 B

ALP6szJY…eEPSo5sX ANwk5Sah…jQDxNmVi

e294807456f770…caef27670a14db

1 in → 2 out8.2900 XPM226 B

AHUuqYqY…MiGd9fP5 AXhWtbPt…5LyuGMVA

533d3b95c7cfcc…7dcc59797fd0ca

1 in → 2 out8.2900 XPM226 B

AQLFcQTM…Qjrb3B9h AZaP8Jpw…37x6Ao45

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.

1.620 × 10⁹⁸(99-digit number)

16208913046100031901…47637537763942727679

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

1.620 × 10⁹⁸(99-digit number)

16208913046100031901…47637537763942727679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.620 × 10⁹⁸(99-digit number)

16208913046100031901…47637537763942727681

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

3.241 × 10⁹⁸(99-digit number)

32417826092200063803…95275075527885455359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.241 × 10⁹⁸(99-digit number)

32417826092200063803…95275075527885455361

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

6.483 × 10⁹⁸(99-digit number)

64835652184400127606…90550151055770910719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.483 × 10⁹⁸(99-digit number)

64835652184400127606…90550151055770910721

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

1.296 × 10⁹⁹(100-digit number)

12967130436880025521…81100302111541821439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.296 × 10⁹⁹(100-digit number)

12967130436880025521…81100302111541821441

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

2.593 × 10⁹⁹(100-digit number)

25934260873760051042…62200604223083642879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.593 × 10⁹⁹(100-digit number)

25934260873760051042…62200604223083642881

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

5.186 × 10⁹⁹(100-digit number)

51868521747520102084…24401208446167285759

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 #877,683

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