Block #1,122,132

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/22/2015, 2:54:52 AM · Difficulty 10.9399 · 5,686,806 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cda371b0c7049d87c2ea100c41ac8454d62b4ebbe0c2ac91a24ac5e24b2f1d92

View on Chainz ↗

Height

#1,122,132

Difficulty

10.939938

Transactions

Size

7.64 KB

Version

Bits

0af09fc2

Nonce

362,361,249

Timestamp

6/22/2015, 2:54:52 AM

Confirmations

5,686,806

Mined by

⛏️ P2SHAG8Rt21E1sfxX3ZvGV62bYGQJHMARNjR7q

Merkle Root

9e542cf7fc21434149284347d2e805ff214fd04d1061399c34d52b971551354c

Transactions (2)

Coinbase5b54e42e06838f…db058ee7a70d05

1 in → 1 out8.5100 XPM110 B

AG8Rt21E…MARNjR7q

59ea796ebfa22d…7cff0dc37fe7cf

51 in → 2 out1434.9404 XPM7.44 KB

ASyJThhK…vhpEpzJt AaxCzsay…bAqhqJEy

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.

2.673 × 10⁹⁴(95-digit number)

26737843046675665302…45975247679238865279

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

2.673 × 10⁹⁴(95-digit number)

26737843046675665302…45975247679238865279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.673 × 10⁹⁴(95-digit number)

26737843046675665302…45975247679238865281

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

5.347 × 10⁹⁴(95-digit number)

53475686093351330605…91950495358477730559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.347 × 10⁹⁴(95-digit number)

53475686093351330605…91950495358477730561

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

1.069 × 10⁹⁵(96-digit number)

10695137218670266121…83900990716955461119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.069 × 10⁹⁵(96-digit number)

10695137218670266121…83900990716955461121

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

2.139 × 10⁹⁵(96-digit number)

21390274437340532242…67801981433910922239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.139 × 10⁹⁵(96-digit number)

21390274437340532242…67801981433910922241

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

4.278 × 10⁹⁵(96-digit number)

42780548874681064484…35603962867821844479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.278 × 10⁹⁵(96-digit number)

42780548874681064484…35603962867821844481

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.556 × 10⁹⁵(96-digit number)

85561097749362128968…71207925735643688959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,122,132

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