Block #1,506,932

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2016, 12:07:22 AM · Difficulty 10.6311 · 5,331,574 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d160a72c4847d9e06a439612ccd62735e3bfa27b4771f52b24e21351a5528e6d

View on Chainz ↗

Height

#1,506,932

Difficulty

10.631126

Transactions

Size

799 B

Version

Bits

0aa19177

Nonce

174,498,319

Timestamp

3/22/2016, 12:07:22 AM

Confirmations

5,331,574

Mined by

⛏️ P2SHAXzSVE4gcTpgaXyCE18BuUqUZM6eUnXxQB

Merkle Root

4203b442a51da5105fb333bd8c239dc50c01e4ae892ff32598f4af001169e742

Transactions (2)

Coinbase6326a1fee99ed2…370621d06e5a72

1 in → 1 out8.8400 XPM110 B

AXzSVE4g…6eUnXxQB

7e36e3d716780e…000f2ccfc07b01

1 in → 13 out194.8843 XPM599 B

Ae9wYuZx…WqNFE1D7 AGezuDgF…Rc1c725a AH8sqRJw…oV88VbpT AW6zRY4z…ELnj21DS ALjKTp6g…7U8d2jxD

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.

3.564 × 10⁹⁴(95-digit number)

35640188961082914133…78356578647641829119

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

3.564 × 10⁹⁴(95-digit number)

35640188961082914133…78356578647641829119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.564 × 10⁹⁴(95-digit number)

35640188961082914133…78356578647641829121

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

7.128 × 10⁹⁴(95-digit number)

71280377922165828267…56713157295283658239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.128 × 10⁹⁴(95-digit number)

71280377922165828267…56713157295283658241

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

1.425 × 10⁹⁵(96-digit number)

14256075584433165653…13426314590567316479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.425 × 10⁹⁵(96-digit number)

14256075584433165653…13426314590567316481

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

2.851 × 10⁹⁵(96-digit number)

28512151168866331307…26852629181134632959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.851 × 10⁹⁵(96-digit number)

28512151168866331307…26852629181134632961

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

5.702 × 10⁹⁵(96-digit number)

57024302337732662614…53705258362269265919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.702 × 10⁹⁵(96-digit number)

57024302337732662614…53705258362269265921

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 #1,506,932

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