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Block #447,699

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/17/2014, 10:52:12 AM Β· Difficulty 10.3610 Β· 6,359,498 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f86d7a0f7b100ee3a9e6c48642696f4597ab462019b0e1b35272bf0167ef026c
View on Chainz β†—

Height

#447,699

Difficulty

10.361031

Transactions

1

Size

200 B

Version

2

Bits

0a5c6c87

Nonce

441,098

Timestamp

3/17/2014, 10:52:12 AM

Confirmations

6,359,498

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a0cfe8027a2e29db7eb64b0d538ae086af050bb70192580f69cf675766630d0f
Transactions (1)
Coinbasea0cfe8027a2e29…cf675766630d0f
1 in β†’ 1 out9.3000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.726 Γ— 10⁹⁡(96-digit number)
27265742176159018135…88256861878642931659
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
2.726 Γ— 10⁹⁡(96-digit number)
27265742176159018135…88256861878642931659
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.726 Γ— 10⁹⁡(96-digit number)
27265742176159018135…88256861878642931661
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
5.453 Γ— 10⁹⁡(96-digit number)
54531484352318036271…76513723757285863319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.453 Γ— 10⁹⁡(96-digit number)
54531484352318036271…76513723757285863321
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
1.090 Γ— 10⁹⁢(97-digit number)
10906296870463607254…53027447514571726639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.090 Γ— 10⁹⁢(97-digit number)
10906296870463607254…53027447514571726641
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
2.181 Γ— 10⁹⁢(97-digit number)
21812593740927214508…06054895029143453279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.181 Γ— 10⁹⁢(97-digit number)
21812593740927214508…06054895029143453281
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
4.362 Γ— 10⁹⁢(97-digit number)
43625187481854429017…12109790058286906559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.362 Γ— 10⁹⁢(97-digit number)
43625187481854429017…12109790058286906561
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:57,701,589 XPMΒ·at block #6,807,196 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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