Block #1,426,835

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2016, 10:04:37 PM · Difficulty 10.7543 · 5,415,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

80af34150763ab5c350d6b17c7711c277baf3f3520e5db9cded5cf99364edd63

View on Chainz ↗

Height

#1,426,835

Difficulty

10.754299

Transactions

Size

868 B

Version

Bits

0ac119c4

Nonce

862,900,598

Timestamp

1/24/2016, 10:04:37 PM

Confirmations

5,415,243

Mined by

⛏️ P2SHALCvqxDn1whjYeQMBLXuimb2BvSDM4dVbA

Merkle Root

581dae27fcc3d441260e8ce86502d2ee139e6fef2fda649ce1da8b07502c6e20

Transactions (2)

Coinbase2f16f390fcea0e…264ad55aae4588

1 in → 1 out8.6400 XPM109 B

ALCvqxDn…SDM4dVbA

fd30e03a2c57a3…bb6c2b6cf0460f

1 in → 15 out232.9782 XPM668 B

AUhLZdsR…gKMfjeDb AK8zaMgH…bkyU6462 ANsRsXKA…8mfksanZ AZsdqwDB…MupLuX3j ARB6qyYM…UfzKMJj1

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.

2.664 × 10⁹⁶(97-digit number)

26648544146410980242…07938610148439613439

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

2.664 × 10⁹⁶(97-digit number)

26648544146410980242…07938610148439613439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.664 × 10⁹⁶(97-digit number)

26648544146410980242…07938610148439613441

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

5.329 × 10⁹⁶(97-digit number)

53297088292821960484…15877220296879226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.329 × 10⁹⁶(97-digit number)

53297088292821960484…15877220296879226881

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

1.065 × 10⁹⁷(98-digit number)

10659417658564392096…31754440593758453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.065 × 10⁹⁷(98-digit number)

10659417658564392096…31754440593758453761

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

2.131 × 10⁹⁷(98-digit number)

21318835317128784193…63508881187516907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.131 × 10⁹⁷(98-digit number)

21318835317128784193…63508881187516907521

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

4.263 × 10⁹⁷(98-digit number)

42637670634257568387…27017762375033815039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.263 × 10⁹⁷(98-digit number)

42637670634257568387…27017762375033815041

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 #1,426,835

Cookie Preferences