Block #876,577

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2014, 12:01:33 PM · Difficulty 10.9645 · 5,917,617 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f0aa1827e68966662b81275211881af110f87541dfbd5a5f274b6a2610d0327

View on Chainz ↗

Height

#876,577

Difficulty

10.964543

Transactions

Size

393 B

Version

Bits

0af6ec4e

Nonce

1,656,311,641

Timestamp

12/31/2014, 12:01:33 PM

Confirmations

5,917,617

Merkle Root

e02856fb58e25669f4ed577be944d14c8da060d4a3500f297a9bcc9332e8a634

Transactions (2)

Coinbase14f4d8317ea5ea…05eccc6fa7ee0f

1 in → 1 out8.3100 XPM109 B

AVdmRGV5…dwzJe4Lh

9c63694d7d64e6…0232d4d0a9cd8c

1 in → 1 out5.0191 XPM193 B

ASLwqNEo…1ccEZYHV

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.

1.988 × 10⁹⁶(97-digit number)

19887664560586172128…12959660586335842239

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

1.988 × 10⁹⁶(97-digit number)

19887664560586172128…12959660586335842239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.988 × 10⁹⁶(97-digit number)

19887664560586172128…12959660586335842241

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

3.977 × 10⁹⁶(97-digit number)

39775329121172344257…25919321172671684479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.977 × 10⁹⁶(97-digit number)

39775329121172344257…25919321172671684481

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

7.955 × 10⁹⁶(97-digit number)

79550658242344688515…51838642345343368959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.955 × 10⁹⁶(97-digit number)

79550658242344688515…51838642345343368961

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

1.591 × 10⁹⁷(98-digit number)

15910131648468937703…03677284690686737919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.591 × 10⁹⁷(98-digit number)

15910131648468937703…03677284690686737921

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

3.182 × 10⁹⁷(98-digit number)

31820263296937875406…07354569381373475839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.182 × 10⁹⁷(98-digit number)

31820263296937875406…07354569381373475841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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