Block #486,646

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 5:15:14 PM · Difficulty 10.6291 · 6,319,664 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c32ec00629d9e20e2a6103d048f2b0ebf5716b918a30748a8f3bbbc8f2c8c2db

View on Chainz ↗

Height

#486,646

Difficulty

10.629057

Transactions

Size

1.04 KB

Version

Bits

0aa109e1

Nonce

314,561,941

Timestamp

4/11/2014, 5:15:14 PM

Confirmations

6,319,664

Mined by

⛏️ P2SHAaC1dPQLCZuo1AQQHHxFSm9FQb2ugioj6o

Merkle Root

8660c2e506f73e2108bd6dd64b3dae99520871244b56b3989e63372b2c381c1d

Transactions (4)

Coinbaseb1ab96583c2198…1963976a7d46b3

1 in → 1 out8.8700 XPM111 B

AaC1dPQL…2ugioj6o

84a88eb8ff2a3b…2fbe52493af1e8

2 in → 4 out12.5797 XPM408 B

AXSSYByb…8vG2sYWV AWkTY9wW…HrBW1npq AcBvLaSu…X3gaHvJ1 AeKNrjNj…1NEq95Ta

91caa68fc98a0f…7ad773632c605d

1 in → 2 out5.8702 XPM225 B

ALd9joYT…AMHjiFdt AMU8nEj9…Eo32pqxr

c22557fcf4ba4c…67e51efbaf808e

1 in → 2 out1.4528 XPM225 B

AWPqEoVY…vFtzFvew AMdkZdpH…aiMe3RNJ

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.

1.565 × 10⁹⁹(100-digit number)

15652928451047600158…27513001743574199039

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

1.565 × 10⁹⁹(100-digit number)

15652928451047600158…27513001743574199039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.565 × 10⁹⁹(100-digit number)

15652928451047600158…27513001743574199041

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

3.130 × 10⁹⁹(100-digit number)

31305856902095200317…55026003487148398079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.130 × 10⁹⁹(100-digit number)

31305856902095200317…55026003487148398081

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

6.261 × 10⁹⁹(100-digit number)

62611713804190400635…10052006974296796159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.261 × 10⁹⁹(100-digit number)

62611713804190400635…10052006974296796161

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

1.252 × 10¹⁰⁰(101-digit number)

12522342760838080127…20104013948593592319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.252 × 10¹⁰⁰(101-digit number)

12522342760838080127…20104013948593592321

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

2.504 × 10¹⁰⁰(101-digit number)

25044685521676160254…40208027897187184639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.504 × 10¹⁰⁰(101-digit number)

25044685521676160254…40208027897187184641

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 #486,646

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