Block #2,185,622

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/30/2017, 2:06:08 AM · Difficulty 10.9450 · 4,653,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ffac6710160ff1610dcfe53826d1f7e3ed03de08487aa7bed26c2583b1efc01

View on Chainz ↗

Height

#2,185,622

Difficulty

10.944967

Transactions

Size

424 B

Version

Bits

0af1e956

Nonce

1,417,779,455

Timestamp

6/30/2017, 2:06:08 AM

Confirmations

4,653,173

Mined by

⛏️ P2SHAJEo5RSMK2RgKgDDTvrjsQeyiCJ82QDJhk

Merkle Root

d893b58603c71c444226e149db7222787a1405355a2f9dd68912a6983aa8373a

Transactions (2)

Coinbaseca56822b4f0036…9ccd1de8f9f843

1 in → 1 out8.3400 XPM110 B

AJEo5RSM…J82QDJhk

b76e398eee3a15…8ef51cfa008a5e

1 in → 2 out205728.4630 XPM225 B

AMNqyy2W…ise9w8w1 AFsDnZbN…tC8rWDoS

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.

4.353 × 10⁹²(93-digit number)

43535640184528821563…07535324906394555159

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

4.353 × 10⁹²(93-digit number)

43535640184528821563…07535324906394555159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.353 × 10⁹²(93-digit number)

43535640184528821563…07535324906394555161

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

8.707 × 10⁹²(93-digit number)

87071280369057643127…15070649812789110319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.707 × 10⁹²(93-digit number)

87071280369057643127…15070649812789110321

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

1.741 × 10⁹³(94-digit number)

17414256073811528625…30141299625578220639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.741 × 10⁹³(94-digit number)

17414256073811528625…30141299625578220641

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

3.482 × 10⁹³(94-digit number)

34828512147623057251…60282599251156441279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.482 × 10⁹³(94-digit number)

34828512147623057251…60282599251156441281

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

6.965 × 10⁹³(94-digit number)

69657024295246114502…20565198502312882559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.965 × 10⁹³(94-digit number)

69657024295246114502…20565198502312882561

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 #2,185,622

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