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Block #469,998

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/1/2014, 2:49:59 PM Β· Difficulty 10.4297 Β· 6,372,684 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0f434889d0e7f0d7a6f0139c7b50293a5bf6bc11529e1a06204e60347d557dbd
View on Chainz β†—

Height

#469,998

Difficulty

10.429660

Transactions

1

Size

200 B

Version

2

Bits

0a6dfe2b

Nonce

29,909,412

Timestamp

4/1/2014, 2:49:59 PM

Confirmations

6,372,684

Mined by

⛏️ P2SHATv6hjkuGsKx9rMnwYtx1TXpY8D48Sz3Lh

Merkle Root

6f9fad4cdc707e416f42e6210be2f406c034ebf13af5058e01e9ddc8c8b3a568
Transactions (1)
Coinbase6f9fad4cdc707e…e9ddc8c8b3a568
1 in β†’ 1 out9.1800 XPM109 B
ATv6hjku…D48Sz3Lh
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.

2.922 Γ— 10⁹⁢(97-digit number)
29228402080317437594…82185442041699764479
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
2.922 Γ— 10⁹⁢(97-digit number)
29228402080317437594…82185442041699764479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.922 Γ— 10⁹⁢(97-digit number)
29228402080317437594…82185442041699764481
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
5.845 Γ— 10⁹⁢(97-digit number)
58456804160634875189…64370884083399528959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.845 Γ— 10⁹⁢(97-digit number)
58456804160634875189…64370884083399528961
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
1.169 Γ— 10⁹⁷(98-digit number)
11691360832126975037…28741768166799057919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.169 Γ— 10⁹⁷(98-digit number)
11691360832126975037…28741768166799057921
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
2.338 Γ— 10⁹⁷(98-digit number)
23382721664253950075…57483536333598115839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.338 Γ— 10⁹⁷(98-digit number)
23382721664253950075…57483536333598115841
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
4.676 Γ— 10⁹⁷(98-digit number)
46765443328507900151…14967072667196231679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.676 Γ— 10⁹⁷(98-digit number)
46765443328507900151…14967072667196231681
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:57,985,802 XPMΒ·at block #6,842,681 Β· updates every 60s
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