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Block #442,169

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/13/2014, 3:38:33 PM Β· Difficulty 10.3504 Β· 6,365,860 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0f060a64bd50bee53a8197fc496cb5c9ec79de2cb8dca7feb30327f5bb479b9c
View on Chainz β†—

Height

#442,169

Difficulty

10.350405

Transactions

1

Size

206 B

Version

2

Bits

0a59b425

Nonce

218,106,267

Timestamp

3/13/2014, 3:38:33 PM

Confirmations

6,365,860

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d64aa5f1f4d49191f450f82109c496696f4f2a2f6d6dd0f58289e0a4bfac5032
Transactions (1)
Coinbased64aa5f1f4d491…89e0a4bfac5032
1 in β†’ 1 out9.3200 XPM116 B
AbwWkWZt…kawDhufa
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.

7.989 Γ— 10⁹⁴(95-digit number)
79896010186656599554…48654127033340676959
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
7.989 Γ— 10⁹⁴(95-digit number)
79896010186656599554…48654127033340676959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.989 Γ— 10⁹⁴(95-digit number)
79896010186656599554…48654127033340676961
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
1.597 Γ— 10⁹⁡(96-digit number)
15979202037331319910…97308254066681353919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.597 Γ— 10⁹⁡(96-digit number)
15979202037331319910…97308254066681353921
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
3.195 Γ— 10⁹⁡(96-digit number)
31958404074662639821…94616508133362707839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.195 Γ— 10⁹⁡(96-digit number)
31958404074662639821…94616508133362707841
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
6.391 Γ— 10⁹⁡(96-digit number)
63916808149325279643…89233016266725415679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.391 Γ— 10⁹⁡(96-digit number)
63916808149325279643…89233016266725415681
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
1.278 Γ— 10⁹⁢(97-digit number)
12783361629865055928…78466032533450831359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.278 Γ— 10⁹⁢(97-digit number)
12783361629865055928…78466032533450831361
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:57,708,276 XPMΒ·at block #6,808,028 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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