Block #1,499,557

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/16/2016, 7:06:20 PM · Difficulty 10.6398 · 5,339,948 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c623a9f022317f0d34ac121f3e6537074158f31b85c75324d0c17e31231b7535

View on Chainz ↗

Height

#1,499,557

Difficulty

10.639847

Transactions

Size

1.51 KB

Version

Bits

0aa3cd03

Nonce

23,681,223

Timestamp

3/16/2016, 7:06:20 PM

Confirmations

5,339,948

Mined by

⛏️ P2SHALsi6neaN9a4ivDSyJ51tgjqKywLYXbeTv

Merkle Root

93c815be0413cd48a4527f9bc3f501f67fecd229ddb109e6b7874a940708bfd8

Transactions (2)

Coinbasec5e112e6f98292…1471b5932d9282

1 in → 1 out8.8400 XPM109 B

ALsi6nea…wLYXbeTv

96bfc437b79af4…874f54047e2723

1 in → 35 out71.4234 XPM1.32 KB

Ab3iAy41…yzTwRb8a AUf8Sixq…SUoEoccN AGxnnLba…YSrzGyx3 Aa7Xu2Sh…Wj171Mhv Ae9wYuZx…WqNFE1D7

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.

3.479 × 10⁹⁸(99-digit number)

34797739777577618221…66247309749807349759

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

3.479 × 10⁹⁸(99-digit number)

34797739777577618221…66247309749807349759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.479 × 10⁹⁸(99-digit number)

34797739777577618221…66247309749807349761

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

6.959 × 10⁹⁸(99-digit number)

69595479555155236442…32494619499614699519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.959 × 10⁹⁸(99-digit number)

69595479555155236442…32494619499614699521

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

1.391 × 10⁹⁹(100-digit number)

13919095911031047288…64989238999229399039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.391 × 10⁹⁹(100-digit number)

13919095911031047288…64989238999229399041

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

2.783 × 10⁹⁹(100-digit number)

27838191822062094576…29978477998458798079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.783 × 10⁹⁹(100-digit number)

27838191822062094576…29978477998458798081

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

5.567 × 10⁹⁹(100-digit number)

55676383644124189153…59956955996917596159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.567 × 10⁹⁹(100-digit number)

55676383644124189153…59956955996917596161

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

1.113 × 10¹⁰⁰(101-digit number)

11135276728824837830…19913911993835192319

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 #1,499,557

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