Block #2,213,034

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/19/2017, 5:59:21 AM · Difficulty 10.9439 · 4,613,761 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1197bfebd88e8182450a2c4f3ae49796b58b512ba68c78c746a04efc158f4243

View on Chainz ↗

Height

#2,213,034

Difficulty

10.943878

Transactions

Size

424 B

Version

Bits

0af1a1f7

Nonce

288,811,431

Timestamp

7/19/2017, 5:59:21 AM

Confirmations

4,613,761

Mined by

⛏️ P2SHASXBGvreRGZYvoqcUcMTY8brHbkJo4Gzfu

Merkle Root

f707c9db9ce43dccb4346dc6998b98effc14a08be55d970de2ce33f24685f7d7

Transactions (2)

Coinbase8ed0a4516748c1…4c140764f81ed7

1 in → 1 out8.3500 XPM109 B

ASXBGvre…kJo4Gzfu

c398c1ff7f0e6f…0714235ad94f72

1 in → 2 out144606.9024 XPM226 B

AecRgBfB…G3EEbqBL AJySnNqu…3adXwvuc

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.

1.003 × 10⁹²(93-digit number)

10035983125571394571…07798684046992687999

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

1.003 × 10⁹²(93-digit number)

10035983125571394571…07798684046992687999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.003 × 10⁹²(93-digit number)

10035983125571394571…07798684046992688001

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

2.007 × 10⁹²(93-digit number)

20071966251142789142…15597368093985375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.007 × 10⁹²(93-digit number)

20071966251142789142…15597368093985376001

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

4.014 × 10⁹²(93-digit number)

40143932502285578285…31194736187970751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.014 × 10⁹²(93-digit number)

40143932502285578285…31194736187970752001

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

8.028 × 10⁹²(93-digit number)

80287865004571156570…62389472375941503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.028 × 10⁹²(93-digit number)

80287865004571156570…62389472375941504001

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

1.605 × 10⁹³(94-digit number)

16057573000914231314…24778944751883007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.605 × 10⁹³(94-digit number)

16057573000914231314…24778944751883008001

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

3.211 × 10⁹³(94-digit number)

32115146001828462628…49557889503766015999

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 #2,213,034

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