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Block #431,218

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/6/2014, 1:41:06 AM Β· Difficulty 10.3404 Β· 6,377,177 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca88f7baf68201d301e392de5ab95df0f940f7199aa6e7452ce0b536c4dd85bd
View on Chainz β†—

Height

#431,218

Difficulty

10.340359

Transactions

2

Size

870 B

Version

2

Bits

0a5721c4

Nonce

312,857

Timestamp

3/6/2014, 1:41:06 AM

Confirmations

6,377,177

Mined by

⛏️ P2SHAL9zJ2xXaEYhGvHhcWfKLcVACzLuZQYBB8

Merkle Root

cdec5cc17062e1f21e915ea81d626025229bc19b6068e7fcf99c35c10ff19131
Transactions (2)
Coinbasee57afaa33116e3…009796c937b84a
1 in β†’ 1 out9.3500 XPM109 B
AL9zJ2xX…LuZQYBB8
24adef5ad749af…0e07dbf6bf7add
4 in β†’ 2 out0.9317 XPM670 B
ANA654SS…XXR89mDnAMqDar8h…42tvSFxj
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.

2.287 Γ— 10⁹⁷(98-digit number)
22874646469695229828…82790194834624582079
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
2.287 Γ— 10⁹⁷(98-digit number)
22874646469695229828…82790194834624582079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.287 Γ— 10⁹⁷(98-digit number)
22874646469695229828…82790194834624582081
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
4.574 Γ— 10⁹⁷(98-digit number)
45749292939390459657…65580389669249164159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.574 Γ— 10⁹⁷(98-digit number)
45749292939390459657…65580389669249164161
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
9.149 Γ— 10⁹⁷(98-digit number)
91498585878780919314…31160779338498328319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.149 Γ— 10⁹⁷(98-digit number)
91498585878780919314…31160779338498328321
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
1.829 Γ— 10⁹⁸(99-digit number)
18299717175756183862…62321558676996656639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.829 Γ— 10⁹⁸(99-digit number)
18299717175756183862…62321558676996656641
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
3.659 Γ— 10⁹⁸(99-digit number)
36599434351512367725…24643117353993313279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.659 Γ— 10⁹⁸(99-digit number)
36599434351512367725…24643117353993313281
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:57,711,216 XPMΒ·at block #6,808,394 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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