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Block #208,373

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/13/2013, 11:27:29 PM Β· Difficulty 9.9061 Β· 6,602,228 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bb0144b78fc9e2ad615462c5806786531a370872e7fd92649a4079e02ff924d6
View on Chainz β†—

Height

#208,373

Difficulty

9.906120

Transactions

1

Size

198 B

Version

2

Bits

09e7f783

Nonce

24,163

Timestamp

10/13/2013, 11:27:29 PM

Confirmations

6,602,228

Mined by

⛏️ P2SHAXKgkkDGrogBEHJHSetHJnSBPfJyE5mk6Y

Merkle Root

f771f271e5d91996fe645a6414cfcb73e3e14931f31d2fbbeb8c25cf85941558
Transactions (1)
Coinbasef771f271e5d919…8c25cf85941558
1 in β†’ 1 out10.1800 XPM109 B
AXKgkkDG…JyE5mk6Y
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.

3.858 Γ— 10⁹²(93-digit number)
38585177733675258759…17171304569113241599
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
3.858 Γ— 10⁹²(93-digit number)
38585177733675258759…17171304569113241599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.858 Γ— 10⁹²(93-digit number)
38585177733675258759…17171304569113241601
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
7.717 Γ— 10⁹²(93-digit number)
77170355467350517519…34342609138226483199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.717 Γ— 10⁹²(93-digit number)
77170355467350517519…34342609138226483201
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
1.543 Γ— 10⁹³(94-digit number)
15434071093470103503…68685218276452966399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.543 Γ— 10⁹³(94-digit number)
15434071093470103503…68685218276452966401
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
3.086 Γ— 10⁹³(94-digit number)
30868142186940207007…37370436552905932799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.086 Γ— 10⁹³(94-digit number)
30868142186940207007…37370436552905932801
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
6.173 Γ— 10⁹³(94-digit number)
61736284373880414015…74740873105811865599
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,728,896 XPMΒ·at block #6,810,600 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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