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Block #210,867

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/15/2013, 10:08:42 AM Β· Difficulty 9.9137 Β· 6,602,182 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0aa144ad521586d095e0d7900326125a153b4c8b766e8022ba4be2ddb8ffe335
View on Chainz β†—

Height

#210,867

Difficulty

9.913666

Transactions

1

Size

199 B

Version

2

Bits

09e9e601

Nonce

52,161

Timestamp

10/15/2013, 10:08:42 AM

Confirmations

6,602,182

Mined by

⛏️ P2SHAWP61hEiaZm3DZc3hxZMaedUsm1dnDFsZW

Merkle Root

978ea703202cc40bfc31cd941f6a91c5cd6eae063ac5c5dc2ba5f117bd5da570
Transactions (1)
Coinbase978ea703202cc4…a5f117bd5da570
1 in β†’ 1 out10.1600 XPM109 B
AWP61hEi…1dnDFsZW
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.459 Γ— 10⁹⁴(95-digit number)
14598752032522364437…21347568874854147359
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.459 Γ— 10⁹⁴(95-digit number)
14598752032522364437…21347568874854147359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.459 Γ— 10⁹⁴(95-digit number)
14598752032522364437…21347568874854147361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.919 Γ— 10⁹⁴(95-digit number)
29197504065044728875…42695137749708294719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.919 Γ— 10⁹⁴(95-digit number)
29197504065044728875…42695137749708294721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.839 Γ— 10⁹⁴(95-digit number)
58395008130089457751…85390275499416589439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.839 Γ— 10⁹⁴(95-digit number)
58395008130089457751…85390275499416589441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.167 Γ— 10⁹⁡(96-digit number)
11679001626017891550…70780550998833178879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.167 Γ— 10⁹⁡(96-digit number)
11679001626017891550…70780550998833178881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.335 Γ— 10⁹⁡(96-digit number)
23358003252035783100…41561101997666357759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.335 Γ— 10⁹⁡(96-digit number)
23358003252035783100…41561101997666357761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,748,437 XPMΒ·at block #6,813,048 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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