Block #292,001

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 12:09:11 PM · Difficulty 9.9901 · 6,517,747 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

857dbcdef8d1105f0dc180a8d054cdb1023b0970f22b91f75e49f599407c1bce

View on Chainz ↗

Height

#292,001

Difficulty

9.990097

Transactions

Size

767 B

Version

Bits

09fd76fa

Nonce

176,457

Timestamp

12/3/2013, 12:09:11 PM

Confirmations

6,517,747

Mined by

⛏️ taRAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

f260c3f3749360a79c589d1c9bdf8b040027ea42c7dcacc26fe0f3af177142fe

Transactions (1)

Coinbasef260c3f3749360…e0f3af177142fe

1 in → 18 out10.0000 XPM675 B

AZninDSu…FvgDMwC4 AKde1i4d…88R1bw6g Ab9NZWSq…3UkdcwAB AJzWx2VD…j4ZSMit5 AZ2pPuKg…95SN2Yr7

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.

2.297 × 10⁹⁹(100-digit number)

22975170723832953189…94374002577825791999

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

2.297 × 10⁹⁹(100-digit number)

22975170723832953189…94374002577825791999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.297 × 10⁹⁹(100-digit number)

22975170723832953189…94374002577825792001

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

4.595 × 10⁹⁹(100-digit number)

45950341447665906378…88748005155651583999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.595 × 10⁹⁹(100-digit number)

45950341447665906378…88748005155651584001

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

9.190 × 10⁹⁹(100-digit number)

91900682895331812757…77496010311303167999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.190 × 10⁹⁹(100-digit number)

91900682895331812757…77496010311303168001

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

1.838 × 10¹⁰⁰(101-digit number)

18380136579066362551…54992020622606335999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.838 × 10¹⁰⁰(101-digit number)

18380136579066362551…54992020622606336001

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

3.676 × 10¹⁰⁰(101-digit number)

36760273158132725103…09984041245212671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.676 × 10¹⁰⁰(101-digit number)

36760273158132725103…09984041245212672001

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 #292,001

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