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Block #441,427

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/13/2014, 3:17:11 AM Β· Difficulty 10.3500 Β· 6,369,708 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e6be35d834147f77361827a22aabb8167c821b92c0ffd8a3a44ac9ae9f064109
View on Chainz β†—

Height

#441,427

Difficulty

10.349978

Transactions

2

Size

6.02 KB

Version

2

Bits

0a59982b

Nonce

7,482

Timestamp

3/13/2014, 3:17:11 AM

Confirmations

6,369,708

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3aa1f8a8e20e35a7f216349236183c06503fb539a6503cccd54784101f5ed04d
Transactions (2)
Coinbase46ed6c66982852…1493b519a88eda
1 in β†’ 1 out9.3900 XPM116 B
AbwWkWZt…kawDhufa
89dacda6bd4335…5319a196361457
40 in β†’ 1 out10000.0000 XPM5.82 KB
Ae5WFHbn…gBo7rvHr
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.

3.281 Γ— 10⁹⁷(98-digit number)
32811273294840057043…43616543058013445259
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
3.281 Γ— 10⁹⁷(98-digit number)
32811273294840057043…43616543058013445259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.281 Γ— 10⁹⁷(98-digit number)
32811273294840057043…43616543058013445261
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
6.562 Γ— 10⁹⁷(98-digit number)
65622546589680114086…87233086116026890519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.562 Γ— 10⁹⁷(98-digit number)
65622546589680114086…87233086116026890521
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
1.312 Γ— 10⁹⁸(99-digit number)
13124509317936022817…74466172232053781039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.312 Γ— 10⁹⁸(99-digit number)
13124509317936022817…74466172232053781041
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
2.624 Γ— 10⁹⁸(99-digit number)
26249018635872045634…48932344464107562079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.624 Γ— 10⁹⁸(99-digit number)
26249018635872045634…48932344464107562081
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
5.249 Γ— 10⁹⁸(99-digit number)
52498037271744091268…97864688928215124159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.249 Γ— 10⁹⁸(99-digit number)
52498037271744091268…97864688928215124161
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:57,733,188 XPMΒ·at block #6,811,134 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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