Block #208,213

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 9:29:42 PM · Difficulty 9.9053 · 6,600,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d219b8bf80f533b3d5ac9e43c97ed2cc5cf6c237ebf5a0b99bbc9c53d4b39645

View on Chainz ↗

Height

#208,213

Difficulty

9.905330

Transactions

Size

1.65 KB

Version

Bits

09e7c3b9

Nonce

3,720

Timestamp

10/13/2013, 9:29:42 PM

Confirmations

6,600,517

Mined by

⛏️ P2SHAPEcDKBhiwmtCs4uPmnx1PYtaBbvmts2ty

Merkle Root

ba728d0c16c8995711dc8e74735d6e71e4d1c3c5008adf8b5cfeeff3d4389565

Transactions (4)

Coinbased57e6b121d66de…520048b25e0618

1 in → 1 out10.2100 XPM109 B

APEcDKBh…bvmts2ty

36b3d4b26e481e…c3c94ddc3b5ddc

5 in → 2 out51.0100 XPM649 B

Aa4s3Z6Y…Pg1PYaik ASqMWSFQ…LSt4xjB9

bdf876e50ec8bc…8332d937222178

5 in → 2 out50.9500 XPM645 B

ANxcjsiR…5w1WUvBK Aa4s3Z6Y…Pg1PYaik

36a5aac624cd9d…458a788fd9ec2f

1 in → 2 out10.2300 XPM192 B

ANkSBqbE…LajBMwP7 Aa4s3Z6Y…Pg1PYaik

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.

1.386 × 10⁹⁴(95-digit number)

13869606796436739117…71948111649653653919

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

1.386 × 10⁹⁴(95-digit number)

13869606796436739117…71948111649653653919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.386 × 10⁹⁴(95-digit number)

13869606796436739117…71948111649653653921

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

2.773 × 10⁹⁴(95-digit number)

27739213592873478235…43896223299307307839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.773 × 10⁹⁴(95-digit number)

27739213592873478235…43896223299307307841

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

5.547 × 10⁹⁴(95-digit number)

55478427185746956471…87792446598614615679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.547 × 10⁹⁴(95-digit number)

55478427185746956471…87792446598614615681

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

1.109 × 10⁹⁵(96-digit number)

11095685437149391294…75584893197229231359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.109 × 10⁹⁵(96-digit number)

11095685437149391294…75584893197229231361

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

2.219 × 10⁹⁵(96-digit number)

22191370874298782588…51169786394458462719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #208,213

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