Block #488,440

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 5:06:10 PM · Difficulty 10.6551 · 6,324,201 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc3d78f6c59d3da712f79b9b2460825b2d1d5da8d58111318de2958fe89f1458

View on Chainz ↗

Height

#488,440

Difficulty

10.655121

Transactions

Size

1.31 KB

Version

Bits

0aa7b606

Nonce

195,334

Timestamp

4/12/2014, 5:06:10 PM

Confirmations

6,324,201

Mined by

⛏️ sAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

1399d44f393f3efd952bc94cb1a22812ea6fede724e1d8ed6a5013d33bab0e70

Transactions (2)

Coinbaseaff62acc9f5df6…b21e9bf97a08dd

1 in → 22 out8.8000 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb AXCpMYgL…1r94ZQDa AZ34NcPy…8FPeFjPV

809e9080c12c72…c7def28c1f32cc

2 in → 6 out17.7800 XPM441 B

AUkLzhdx…6FJGTCiB AYz3o8Xn…22uacKL1 AcRJhPSS…rM6dyn1m AGw7KuTT…ZfJmwhoB AcBvLaSu…X3gaHvJ1

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.

1.669 × 10¹⁰⁰(101-digit number)

16696319228305481098…76427152867864637439

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

1.669 × 10¹⁰⁰(101-digit number)

16696319228305481098…76427152867864637439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.669 × 10¹⁰⁰(101-digit number)

16696319228305481098…76427152867864637441

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

3.339 × 10¹⁰⁰(101-digit number)

33392638456610962197…52854305735729274879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.339 × 10¹⁰⁰(101-digit number)

33392638456610962197…52854305735729274881

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

6.678 × 10¹⁰⁰(101-digit number)

66785276913221924394…05708611471458549759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.678 × 10¹⁰⁰(101-digit number)

66785276913221924394…05708611471458549761

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

1.335 × 10¹⁰¹(102-digit number)

13357055382644384878…11417222942917099519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.335 × 10¹⁰¹(102-digit number)

13357055382644384878…11417222942917099521

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

2.671 × 10¹⁰¹(102-digit number)

26714110765288769757…22834445885834199039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.671 × 10¹⁰¹(102-digit number)

26714110765288769757…22834445885834199041

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 #488,440

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