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Block #365,544

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/18/2014, 7:59:40 PM Β· Difficulty 10.4244 Β· 6,442,283 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c58ddb0a8fd80938d1df3096bc468bc7dc82a5117e9c30d0c30f048162c66910
View on Chainz β†—

Height

#365,544

Difficulty

10.424394

Transactions

1

Size

188 B

Version

2

Bits

0a6ca51a

Nonce

5,731

Timestamp

1/18/2014, 7:59:40 PM

Confirmations

6,442,283

Mined by

⛏️ aRFANEZwy9tw1DgYw4uGbmja8PNbrE1uf5dKY

Merkle Root

dc03cc8a53640788be6ab11045d218af2b36a7aba9c5c7be0cb72d2d401c190b
Transactions (1)
Coinbasedc03cc8a536407…b72d2d401c190b
1 in β†’ 1 out9.1900 XPM97 B
ANEZwy9t…E1uf5dKY
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.

2.021 Γ— 10⁹⁷(98-digit number)
20212381301074136702…85377385744296325119
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
2.021 Γ— 10⁹⁷(98-digit number)
20212381301074136702…85377385744296325119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.021 Γ— 10⁹⁷(98-digit number)
20212381301074136702…85377385744296325121
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
4.042 Γ— 10⁹⁷(98-digit number)
40424762602148273404…70754771488592650239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.042 Γ— 10⁹⁷(98-digit number)
40424762602148273404…70754771488592650241
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
8.084 Γ— 10⁹⁷(98-digit number)
80849525204296546809…41509542977185300479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.084 Γ— 10⁹⁷(98-digit number)
80849525204296546809…41509542977185300481
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
1.616 Γ— 10⁹⁸(99-digit number)
16169905040859309361…83019085954370600959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.616 Γ— 10⁹⁸(99-digit number)
16169905040859309361…83019085954370600961
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
3.233 Γ— 10⁹⁸(99-digit number)
32339810081718618723…66038171908741201919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.233 Γ— 10⁹⁸(99-digit number)
32339810081718618723…66038171908741201921
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:57,706,651 XPMΒ·at block #6,807,826 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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