Block #1,110,184

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/16/2015, 1:33:51 PM · Difficulty 10.8680 · 5,704,881 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6950069305e3aa6516c5819d58fc29c77171d5f6e5fada685ca0db341c6c4d24

View on Chainz ↗

Height

#1,110,184

Difficulty

10.867964

Transactions

Size

1.57 KB

Version

Bits

0ade32e8

Nonce

69,692,447

Timestamp

6/16/2015, 1:33:51 PM

Confirmations

5,704,881

Mined by

⛏️ P2SHAN5uH1cDKBHvTYoZsoRZ9uuKSZjMG9aR2K

Merkle Root

27c1bd9bedbbd1107cf35250837c2a65ad0ae9d99c18cf0c652e81ad503171c9

Transactions (2)

Coinbase687ca1418e8e22…80e8c582f793dd

1 in → 1 out8.4700 XPM110 B

AN5uH1cD…jMG9aR2K

04592ced659c3d…128d89fc06df53

9 in → 2 out32.5275 XPM1.38 KB

AXvmRBFX…WNfP3L2y AGfh1kfV…LyE1Fxsn

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.

3.465 × 10⁹³(94-digit number)

34657408885756886989…32522219634467352999

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

3.465 × 10⁹³(94-digit number)

34657408885756886989…32522219634467352999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.465 × 10⁹³(94-digit number)

34657408885756886989…32522219634467353001

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

6.931 × 10⁹³(94-digit number)

69314817771513773978…65044439268934705999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.931 × 10⁹³(94-digit number)

69314817771513773978…65044439268934706001

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

1.386 × 10⁹⁴(95-digit number)

13862963554302754795…30088878537869411999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.386 × 10⁹⁴(95-digit number)

13862963554302754795…30088878537869412001

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

2.772 × 10⁹⁴(95-digit number)

27725927108605509591…60177757075738823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.772 × 10⁹⁴(95-digit number)

27725927108605509591…60177757075738824001

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

5.545 × 10⁹⁴(95-digit number)

55451854217211019183…20355514151477647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.545 × 10⁹⁴(95-digit number)

55451854217211019183…20355514151477648001

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 #1,110,184

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