Block #2,119,161

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2017, 1:51:38 PM · Difficulty 10.9100 · 4,693,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1db70d008a960e883fedeacbe47520c8445e37d8ed7f5852a6fceaa63dcc6cf8

View on Chainz ↗

Height

#2,119,161

Difficulty

10.910004

Transactions

Size

10.15 KB

Version

Bits

0ae8f601

Nonce

398,439,720

Timestamp

5/16/2017, 1:51:38 PM

Confirmations

4,693,621

Mined by

⛏️ P2SHATdT7CRBW9C5RG5yrYHQxNfGeaBi3xsm8a

Merkle Root

820aea36cfb0462ec90f6fb97b14d8deeef930f1faa342ce576661476ba9fb06

Transactions (4)

Coinbase50c96d55986ff0…6f02cf1d6f1093

1 in → 1 out8.5100 XPM110 B

ATdT7CRB…Bi3xsm8a

8ae29d5685a4e5…7bea23dd87b6af

1 in → 84 out161.7720 XPM2.94 KB

ASw3bAGE…jqSQV9TK AUkkrmXQ…sv7ELDrq ALpCXBd6…JARbzsEi AGo5NPaF…hcYLCJZ4 AVGfyLfF…tLWPdGbn

372c274e834b6a…0113062b723f9f

1 in → 101 out101.8294 XPM3.51 KB

AJm3T2Pa…SVM2tCuP ALnp16h9…iq4Lnu7e ALbzrbzx…5xDk22Jc AX5tjeiy…SQR4CaHH ALg5YM9o…QpnuxMHq

501dcbdf9194aa…1683ce70e420f3

1 in → 101 out63.3341 XPM3.51 KB

APymbE7o…yWrC9Wz1 AZ2Dv6vs…YoKVyFme ANG3HyUY…LFKWzZCG AePESYQt…AMpyH2bx AS9WBU3y…YoYcUWJr

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.

2.511 × 10⁹⁴(95-digit number)

25111235949059493451…30039384795170313599

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

2.511 × 10⁹⁴(95-digit number)

25111235949059493451…30039384795170313599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.511 × 10⁹⁴(95-digit number)

25111235949059493451…30039384795170313601

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

5.022 × 10⁹⁴(95-digit number)

50222471898118986903…60078769590340627199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.022 × 10⁹⁴(95-digit number)

50222471898118986903…60078769590340627201

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

1.004 × 10⁹⁵(96-digit number)

10044494379623797380…20157539180681254399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.004 × 10⁹⁵(96-digit number)

10044494379623797380…20157539180681254401

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

2.008 × 10⁹⁵(96-digit number)

20088988759247594761…40315078361362508799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.008 × 10⁹⁵(96-digit number)

20088988759247594761…40315078361362508801

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

4.017 × 10⁹⁵(96-digit number)

40177977518495189522…80630156722725017599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.017 × 10⁹⁵(96-digit number)

40177977518495189522…80630156722725017601

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 #2,119,161

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