Block #2,295,927

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/14/2017, 12:17:11 PM · Difficulty 10.9511 · 4,546,909 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

116001c1505d3320c9067c4c48c8ec22baccf64fdbdf1c1127ebac19577eec62

View on Chainz ↗

Height

#2,295,927

Difficulty

10.951080

Transactions

Size

2.58 KB

Version

Bits

0af37a00

Nonce

1,741,207,668

Timestamp

9/14/2017, 12:17:11 PM

Confirmations

4,546,909

Mined by

⛏️ P2SHALZ2yMoRprVPkLCpVbxdTrXHn2QyWCsoaB

Merkle Root

078450a76657440e6a158a3f735d802cacebb923e6808cb5115099cae0a9b432

Transactions (2)

Coinbase1ced967e19dc64…2c4bd5c4030ecc

1 in → 1 out8.3600 XPM110 B

ALZ2yMoR…QyWCsoaB

982124389fbe9e…2c23b323141db9

16 in → 2 out4193.8595 XPM2.39 KB

AViBaKwf…3Xk3qwK8 AcfqDnSg…i1vSHQjb

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.

1.335 × 10⁹⁵(96-digit number)

13355186511730616881…04640918957783159039

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

1.335 × 10⁹⁵(96-digit number)

13355186511730616881…04640918957783159039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.335 × 10⁹⁵(96-digit number)

13355186511730616881…04640918957783159041

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

2.671 × 10⁹⁵(96-digit number)

26710373023461233763…09281837915566318079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.671 × 10⁹⁵(96-digit number)

26710373023461233763…09281837915566318081

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

5.342 × 10⁹⁵(96-digit number)

53420746046922467527…18563675831132636159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.342 × 10⁹⁵(96-digit number)

53420746046922467527…18563675831132636161

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

1.068 × 10⁹⁶(97-digit number)

10684149209384493505…37127351662265272319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.068 × 10⁹⁶(97-digit number)

10684149209384493505…37127351662265272321

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

2.136 × 10⁹⁶(97-digit number)

21368298418768987011…74254703324530544639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.136 × 10⁹⁶(97-digit number)

21368298418768987011…74254703324530544641

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 #2,295,927

Cookie Preferences