Block #2,230,953

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/31/2017, 1:24:47 PM · Difficulty 10.9466 · 4,611,359 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

401408e5fc40bbaeb0a0b6fc34cf1692eee9a6d86f357ec4c8a17d5a751a9232

View on Chainz ↗

Height

#2,230,953

Difficulty

10.946551

Transactions

Size

722 B

Version

Bits

0af2512b

Nonce

287,792,265

Timestamp

7/31/2017, 1:24:47 PM

Confirmations

4,611,359

Mined by

⛏️ P2SHAcJVESbi2ASK1mkrwpmygCEuv88k2rcXcr

Merkle Root

89eb6887b36f0cf016920ba9513ed3d8f27b4c36140fd85569ebadde2eb7e3a0

Transactions (2)

Coinbase39fa6842dd9eb6…b43388d033f9d3

1 in → 1 out8.3400 XPM110 B

AcJVESbi…8k2rcXcr

d0bdd93e0d599b…686e8383af6eec

3 in → 2 out0.5014 XPM522 B

AHmmLTwH…sfykiyzu AX2PxVDy…VP2txVhX

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.

1.221 × 10⁹⁴(95-digit number)

12215667959149521428…14454480925395789439

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

1.221 × 10⁹⁴(95-digit number)

12215667959149521428…14454480925395789439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.221 × 10⁹⁴(95-digit number)

12215667959149521428…14454480925395789441

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

2.443 × 10⁹⁴(95-digit number)

24431335918299042857…28908961850791578879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.443 × 10⁹⁴(95-digit number)

24431335918299042857…28908961850791578881

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

4.886 × 10⁹⁴(95-digit number)

48862671836598085714…57817923701583157759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.886 × 10⁹⁴(95-digit number)

48862671836598085714…57817923701583157761

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

9.772 × 10⁹⁴(95-digit number)

97725343673196171429…15635847403166315519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.772 × 10⁹⁴(95-digit number)

97725343673196171429…15635847403166315521

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

1.954 × 10⁹⁵(96-digit number)

19545068734639234285…31271694806332631039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.954 × 10⁹⁵(96-digit number)

19545068734639234285…31271694806332631041

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 #2,230,953

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