Block #1,023,133

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/19/2015, 6:17:22 AM · Difficulty 10.7531 · 5,787,399 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4e79e71179847df5be000bc087410171cd5890088dbc25167c4927b09b2ed81

View on Chainz ↗

Height

#1,023,133

Difficulty

10.753091

Transactions

Size

652 B

Version

Bits

0ac0ca96

Nonce

757,691,271

Timestamp

4/19/2015, 6:17:22 AM

Confirmations

5,787,399

Mined by

⛏️ P2SHAXzhs3v1j5tzx9aB6cFXWpm95EPXrUASSs

Merkle Root

98267542a3bce333e2d2e15dbbaafc05a6101dbf71612d4e5c7af5d31f133fc0

Transactions (3)

Coinbaseee5b2f1a30c9aa…3441b6ba62ef1d

1 in → 1 out8.6500 XPM109 B

AXzhs3v1…PXrUASSs

0464858b6f0968…e69732d63af047

1 in → 2 out6.9823 XPM226 B

AG3TPGas…cJvesb2o ATuEEYLQ…eCrEssK6

44c20e4d0684e7…c811eefd1f5399

1 in → 2 out5.3705 XPM226 B

Ae7YXEyn…hnSYZsCr AMFeyNfE…9dpL6UYd

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.

1.518 × 10⁹⁶(97-digit number)

15184700948944670638…17645574027131927679

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

1.518 × 10⁹⁶(97-digit number)

15184700948944670638…17645574027131927679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.518 × 10⁹⁶(97-digit number)

15184700948944670638…17645574027131927681

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

3.036 × 10⁹⁶(97-digit number)

30369401897889341276…35291148054263855359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.036 × 10⁹⁶(97-digit number)

30369401897889341276…35291148054263855361

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

6.073 × 10⁹⁶(97-digit number)

60738803795778682553…70582296108527710719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.073 × 10⁹⁶(97-digit number)

60738803795778682553…70582296108527710721

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

1.214 × 10⁹⁷(98-digit number)

12147760759155736510…41164592217055421439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.214 × 10⁹⁷(98-digit number)

12147760759155736510…41164592217055421441

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

2.429 × 10⁹⁷(98-digit number)

24295521518311473021…82329184434110842879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.429 × 10⁹⁷(98-digit number)

24295521518311473021…82329184434110842881

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 #1,023,133

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