Block #837,077

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2014, 1:54:47 PM · Difficulty 10.9759 · 5,980,785 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6018e85e6b7d585387e6d7d39081c5560c6092a1f7e396a185a6b5aff88919f

View on Chainz ↗

Height

#837,077

Difficulty

10.975938

Transactions

Size

244 B

Version

Bits

0af9d70e

Nonce

1,011,709,234

Timestamp

12/2/2014, 1:54:47 PM

Confirmations

5,980,785

Mined by

⛏️ P2SHAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

422a405e5ce944f2eb5d4054f59c7e2f0876ad8b92a5bce4a8278f2b7f701850

Transactions (1)

Coinbase422a405e5ce944…278f2b7f701850

1 in → 2 out8.2900 XPM152 B

AYFivgcJ…FT8wELGF ALPu3s2c…EJXLjVFh

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.

1.079 × 10¹⁰⁰(101-digit number)

10798239132049319003…34931516223505367039

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

1.079 × 10¹⁰⁰(101-digit number)

10798239132049319003…34931516223505367039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.079 × 10¹⁰⁰(101-digit number)

10798239132049319003…34931516223505367041

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

2.159 × 10¹⁰⁰(101-digit number)

21596478264098638007…69863032447010734079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.159 × 10¹⁰⁰(101-digit number)

21596478264098638007…69863032447010734081

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

4.319 × 10¹⁰⁰(101-digit number)

43192956528197276015…39726064894021468159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.319 × 10¹⁰⁰(101-digit number)

43192956528197276015…39726064894021468161

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

8.638 × 10¹⁰⁰(101-digit number)

86385913056394552030…79452129788042936319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.638 × 10¹⁰⁰(101-digit number)

86385913056394552030…79452129788042936321

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

1.727 × 10¹⁰¹(102-digit number)

17277182611278910406…58904259576085872639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.727 × 10¹⁰¹(102-digit number)

17277182611278910406…58904259576085872641

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

Block #837,077

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