Block #353,197

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 7:17:24 PM · Difficulty 10.3220 · 6,455,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be2d027f592c07a58a2a89d57a4f72cff945dd3edbdd47c3c7cdb2f2343af36b

View on Chainz ↗

Height

#353,197

Difficulty

10.321992

Transactions

Size

1.23 KB

Version

Bits

0a526e0e

Nonce

58,170

Timestamp

1/10/2014, 7:17:24 PM

Confirmations

6,455,058

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a73bce81da4e37d054fbbd233b73387f8cc91d9287944740d497523c642d57d5

Transactions (5)

Coinbase2f8ed53f71a657…beb346f21cca2a

1 in → 1 out9.4100 XPM110 B

AeKNrjNj…1NEq95Ta

70c12301522be4…ecb6b9629e6aed

2 in → 2 out10.7012 XPM373 B

AWi2uwNN…xHX5kqAk AVdWroKn…91ESJWXU

495de18bcc97ef…c27b382303a999

1 in → 2 out4.1191 XPM227 B

AXxp24rY…yi3yUFBu AZy5hCHi…FJ112uaH

326bf0a0910ef3…f4093963508a9f

1 in → 2 out3.9311 XPM226 B

ANoc8GRr…L6WooGzJ AaMaxR97…qQnGgZbN

b5358f9678c540…78b6d4c67483bf

1 in → 2 out4.4194 XPM227 B

AavM9ADQ…s5wFV2jY AXtVW2dk…mT83D5oC

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.

1.800 × 10⁹⁹(100-digit number)

18007071730490736324…60806089331020560799

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

1.800 × 10⁹⁹(100-digit number)

18007071730490736324…60806089331020560799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.800 × 10⁹⁹(100-digit number)

18007071730490736324…60806089331020560801

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

3.601 × 10⁹⁹(100-digit number)

36014143460981472648…21612178662041121599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.601 × 10⁹⁹(100-digit number)

36014143460981472648…21612178662041121601

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

7.202 × 10⁹⁹(100-digit number)

72028286921962945296…43224357324082243199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.202 × 10⁹⁹(100-digit number)

72028286921962945296…43224357324082243201

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

1.440 × 10¹⁰⁰(101-digit number)

14405657384392589059…86448714648164486399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.440 × 10¹⁰⁰(101-digit number)

14405657384392589059…86448714648164486401

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

2.881 × 10¹⁰⁰(101-digit number)

28811314768785178118…72897429296328972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.881 × 10¹⁰⁰(101-digit number)

28811314768785178118…72897429296328972801

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 #353,197

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