Block #2,261,855

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/21/2017, 4:58:44 PM · Difficulty 10.9520 · 4,580,295 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f17b811e76a72460950b0d9fa38295eb8133367a9fac588e628beba6d117840d

View on Chainz ↗

Height

#2,261,855

Difficulty

10.951982

Transactions

Size

650 B

Version

Bits

0af3b513

Nonce

101,154,147

Timestamp

8/21/2017, 4:58:44 PM

Confirmations

4,580,295

Mined by

⛏️ P2SHAWsnsTUwNc4bKUv7kBCruZMuja76CCc9w6

Merkle Root

e9eebc0f3165245d0e9a59889cd513075c57ce54b981f60979be573de1da5a8e

Transactions (3)

Coinbase76fa6e33cc521d…20ae58941d00b7

1 in → 1 out8.3400 XPM109 B

AWsnsTUw…76CCc9w6

8a2d5e2ac3e416…e01cca2e096bb8

1 in → 2 out3291.9108 XPM226 B

AVzn1WqH…oMr5YYd4 AeuA49jN…Joy5i6AD

1975d8571ae9a3…b45898cb6d34b0

1 in → 2 out2202.1340 XPM225 B

AS8Swa5k…emSJQqiE AN4onf26…h5sB4tR6

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.

7.851 × 10⁹⁴(95-digit number)

78510954168298851607…84415384570916857839

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

7.851 × 10⁹⁴(95-digit number)

78510954168298851607…84415384570916857839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.851 × 10⁹⁴(95-digit number)

78510954168298851607…84415384570916857841

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

1.570 × 10⁹⁵(96-digit number)

15702190833659770321…68830769141833715679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.570 × 10⁹⁵(96-digit number)

15702190833659770321…68830769141833715681

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

3.140 × 10⁹⁵(96-digit number)

31404381667319540642…37661538283667431359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.140 × 10⁹⁵(96-digit number)

31404381667319540642…37661538283667431361

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

6.280 × 10⁹⁵(96-digit number)

62808763334639081285…75323076567334862719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.280 × 10⁹⁵(96-digit number)

62808763334639081285…75323076567334862721

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

1.256 × 10⁹⁶(97-digit number)

12561752666927816257…50646153134669725439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.256 × 10⁹⁶(97-digit number)

12561752666927816257…50646153134669725441

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 #2,261,855

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