Block #469,777

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 11:27:11 AM · Difficulty 10.4280 · 6,327,085 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4be08617338afbfaf2379b8b6cd24094c647c76d8b9555655d8b677c7846bf0b

View on Chainz ↗

Height

#469,777

Difficulty

10.428014

Transactions

Size

2.28 KB

Version

Bits

0a6d9256

Nonce

406,801

Timestamp

4/1/2014, 11:27:11 AM

Confirmations

6,327,085

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f843408ea16da29bdf2dbf0ad32782c9c447d41454209e7c134ed596e682c143

Transactions (5)

Coinbaseef69db64d0b95b…f6e48767bbefc0

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

46a61ffc5f5c3a…b05e436d017806

2 in → 1 out18.4100 XPM272 B

ANapBLZx…qXfmQB3x

916d6d7a9daa86…c76b89e1800054

9 in → 2 out10.7318 XPM1.38 KB

AViXySsA…VtCHSyeH AY729k79…RevnnqSz

9f2d43b45b4b1d…46b5e4e9d95e90

1 in → 2 out2.3509 XPM225 B

AJBp59Tt…nbWqpAEY AVQNm6sy…JQfndTQv

b2ea5796b10ada…348470e6bce3b8

1 in → 2 out1.6098 XPM225 B

AXnL68UR…jsxeGUhN APtBg3xe…aY2nCqiK

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.

6.626 × 10¹⁰²(103-digit number)

66263051193122419756…01254625936953109439

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

6.626 × 10¹⁰²(103-digit number)

66263051193122419756…01254625936953109439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.626 × 10¹⁰²(103-digit number)

66263051193122419756…01254625936953109441

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

1.325 × 10¹⁰³(104-digit number)

13252610238624483951…02509251873906218879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.325 × 10¹⁰³(104-digit number)

13252610238624483951…02509251873906218881

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

2.650 × 10¹⁰³(104-digit number)

26505220477248967902…05018503747812437759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.650 × 10¹⁰³(104-digit number)

26505220477248967902…05018503747812437761

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

5.301 × 10¹⁰³(104-digit number)

53010440954497935805…10037007495624875519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.301 × 10¹⁰³(104-digit number)

53010440954497935805…10037007495624875521

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

1.060 × 10¹⁰⁴(105-digit number)

10602088190899587161…20074014991249751039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.060 × 10¹⁰⁴(105-digit number)

10602088190899587161…20074014991249751041

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