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Block #343,889

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/4/2014, 11:12:59 PM Β· Difficulty 10.1863 Β· 6,464,256 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
16a94e8bccf04719b55a0c94010bde5e5ff658cc28d406672c74594911b1cb73
View on Chainz β†—

Height

#343,889

Difficulty

10.186284

Transactions

2

Size

427 B

Version

2

Bits

0a2fb049

Nonce

40,058

Timestamp

1/4/2014, 11:12:59 PM

Confirmations

6,464,256

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

87871d3a5581c52402116acd2456ef942b8fd10517e3a1ac5aaad38622945a53
Transactions (2)
Coinbase04277134b27807…b360325b343adb
1 in β†’ 1 out9.6400 XPM110 B
AeKNrjNj…1NEq95Ta
07f6e8b606bb6c…456d9d7bb5cffe
1 in β†’ 2 out0.0500 XPM226 B
AWKhcKD1…AK1RJ4a3AeEGQCg2…8k9uFEqi
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.

1.137 Γ— 10⁹⁸(99-digit number)
11379344704566519648…26783917517021595839
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
1.137 Γ— 10⁹⁸(99-digit number)
11379344704566519648…26783917517021595839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.137 Γ— 10⁹⁸(99-digit number)
11379344704566519648…26783917517021595841
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
2.275 Γ— 10⁹⁸(99-digit number)
22758689409133039296…53567835034043191679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.275 Γ— 10⁹⁸(99-digit number)
22758689409133039296…53567835034043191681
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
4.551 Γ— 10⁹⁸(99-digit number)
45517378818266078592…07135670068086383359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.551 Γ— 10⁹⁸(99-digit number)
45517378818266078592…07135670068086383361
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
9.103 Γ— 10⁹⁸(99-digit number)
91034757636532157185…14271340136172766719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.103 Γ— 10⁹⁸(99-digit number)
91034757636532157185…14271340136172766721
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
1.820 Γ— 10⁹⁹(100-digit number)
18206951527306431437…28542680272345533439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.820 Γ— 10⁹⁹(100-digit number)
18206951527306431437…28542680272345533441
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:57,709,203 XPMΒ·at block #6,808,144 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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