Block #2,167,426

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/19/2017, 1:57:51 PM · Difficulty 10.8981 · 4,641,135 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88070476c880fa7677d70c189a86e94a4b4f90541e4dcb34c0b161701ad42ec0

View on Chainz ↗

Height

#2,167,426

Difficulty

10.898111

Transactions

Size

10.61 KB

Version

Bits

0ae5ea9b

Nonce

910,411,075

Timestamp

6/19/2017, 1:57:51 PM

Confirmations

4,641,135

Mined by

⛏️ P2SHAWPqMVSCru8E19DS2kobGd83iZkxAXXjTw

Merkle Root

cf8bb75d1d3f49a280eaa856835589bd59fe9a24166331b3bd371171217ec3dd

Transactions (3)

Coinbase4d37bac3ebaf8d…cff94584e0a9c6

1 in → 1 out8.5400 XPM109 B

AWPqMVSC…kxAXXjTw

23d4056e6ea1c6…04bc6f9e3354f9

8 in → 1 out159.9700 XPM1.20 KB

AayfzLYB…BQjBqnJw

ebd109219ec6e5…605174977823c5

63 in → 3 out1126.4209 XPM9.21 KB

AZTUk1gx…dDhGnYfb AS1UqLxC…MeJmduyw Ado6kCMv…oCHKJKDm

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.

1.147 × 10⁹⁸(99-digit number)

11474935583001312155…93366647110876856319

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

1.147 × 10⁹⁸(99-digit number)

11474935583001312155…93366647110876856319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.147 × 10⁹⁸(99-digit number)

11474935583001312155…93366647110876856321

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

2.294 × 10⁹⁸(99-digit number)

22949871166002624311…86733294221753712639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.294 × 10⁹⁸(99-digit number)

22949871166002624311…86733294221753712641

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

4.589 × 10⁹⁸(99-digit number)

45899742332005248623…73466588443507425279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.589 × 10⁹⁸(99-digit number)

45899742332005248623…73466588443507425281

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

9.179 × 10⁹⁸(99-digit number)

91799484664010497246…46933176887014850559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.179 × 10⁹⁸(99-digit number)

91799484664010497246…46933176887014850561

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

1.835 × 10⁹⁹(100-digit number)

18359896932802099449…93866353774029701119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.835 × 10⁹⁹(100-digit number)

18359896932802099449…93866353774029701121

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 #2,167,426

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