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Block #446,773

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/16/2014, 7:41:47 PM Β· Difficulty 10.3582 Β· 6,359,287 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
25e1b4d15251ac9ce5b214419657f43296ab7887f43889a170433645134557fd
View on Chainz β†—

Height

#446,773

Difficulty

10.358171

Transactions

2

Size

1.83 KB

Version

2

Bits

0a5bb11d

Nonce

94,424,295

Timestamp

3/16/2014, 7:41:47 PM

Confirmations

6,359,287

Mined by

⛏️ P2SHAbjBgU85BZhrHXmvG9X3cfE45FpWR6qE8T

Merkle Root

36ee8c9ea7c497f93b0b3dd2483a5d87d81017ff1d884ad5f0f4bf789f9fdd84
Transactions (2)
Coinbasee36ec148641331…1deb57b5c36e72
1 in β†’ 1 out9.3300 XPM109 B
AbjBgU85…pWR6qE8T
b03163d358352d…5bcb59f13a5f49
11 in β†’ 1 out33.3563 XPM1.64 KB
AKNyKWYB…oDfopckJ
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.

1.476 Γ— 10⁹⁢(97-digit number)
14764438952390049951…91805427700871824639
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
1.476 Γ— 10⁹⁢(97-digit number)
14764438952390049951…91805427700871824639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.476 Γ— 10⁹⁢(97-digit number)
14764438952390049951…91805427700871824641
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
2.952 Γ— 10⁹⁢(97-digit number)
29528877904780099903…83610855401743649279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.952 Γ— 10⁹⁢(97-digit number)
29528877904780099903…83610855401743649281
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
5.905 Γ— 10⁹⁢(97-digit number)
59057755809560199807…67221710803487298559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.905 Γ— 10⁹⁢(97-digit number)
59057755809560199807…67221710803487298561
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
1.181 Γ— 10⁹⁷(98-digit number)
11811551161912039961…34443421606974597119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.181 Γ— 10⁹⁷(98-digit number)
11811551161912039961…34443421606974597121
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
2.362 Γ— 10⁹⁷(98-digit number)
23623102323824079923…68886843213949194239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.362 Γ— 10⁹⁷(98-digit number)
23623102323824079923…68886843213949194241
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:57,692,564 XPMΒ·at block #6,806,059 Β· updates every 60s
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