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Block #217,844

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/19/2013, 2:27:51 PM Β· Difficulty 9.9290 Β· 6,590,873 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
95bc7813cd5e0d64f07f37a8f9e832bb978c6a0da9b4240877c7db280e9e88c6
View on Chainz β†—

Height

#217,844

Difficulty

9.929007

Transactions

1

Size

204 B

Version

2

Bits

09edd362

Nonce

1,167

Timestamp

10/19/2013, 2:27:51 PM

Confirmations

6,590,873

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

c2decc316d31275039e68672873d408960d3cbdaceb3f85add5cdb1cf2963292
Transactions (1)
Coinbasec2decc316d3127…5cdb1cf2963292
1 in β†’ 1 out10.1300 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.024 Γ— 10⁹⁰(91-digit number)
20247039840582377416…83658299173770572099
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
2.024 Γ— 10⁹⁰(91-digit number)
20247039840582377416…83658299173770572099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.024 Γ— 10⁹⁰(91-digit number)
20247039840582377416…83658299173770572101
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
4.049 Γ— 10⁹⁰(91-digit number)
40494079681164754832…67316598347541144199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.049 Γ— 10⁹⁰(91-digit number)
40494079681164754832…67316598347541144201
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
8.098 Γ— 10⁹⁰(91-digit number)
80988159362329509664…34633196695082288399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.098 Γ— 10⁹⁰(91-digit number)
80988159362329509664…34633196695082288401
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
1.619 Γ— 10⁹¹(92-digit number)
16197631872465901932…69266393390164576799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.619 Γ— 10⁹¹(92-digit number)
16197631872465901932…69266393390164576801
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
3.239 Γ— 10⁹¹(92-digit number)
32395263744931803865…38532786780329153599
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:57,713,781 XPMΒ·at block #6,808,716 Β· updates every 60s
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