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Block #411,454

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/19/2014, 6:48:02 PM Β· Difficulty 10.4290 Β· 6,395,273 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
11d0d02fecd614e2150b66e4a75263683d2d695db56c754066d3b9bb9cf84e52
View on Chainz β†—

Height

#411,454

Difficulty

10.428970

Transactions

1

Size

199 B

Version

2

Bits

0a6dd0f7

Nonce

75,519

Timestamp

2/19/2014, 6:48:02 PM

Confirmations

6,395,273

Mined by

⛏️ P2SHAKgiTbagke9hfkPB2Na9G5N62UMJA8ujWZ

Merkle Root

98e796f8305bad356cf90f91daca503c43b3ab653a0fbf214af578279bbace0d
Transactions (1)
Coinbase98e796f8305bad…f578279bbace0d
1 in β†’ 1 out9.1800 XPM109 B
AKgiTbag…MJA8ujWZ
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.

1.594 Γ— 10⁹⁡(96-digit number)
15947045442961668933…83570181675503084799
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
1.594 Γ— 10⁹⁡(96-digit number)
15947045442961668933…83570181675503084799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.594 Γ— 10⁹⁡(96-digit number)
15947045442961668933…83570181675503084801
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
3.189 Γ— 10⁹⁡(96-digit number)
31894090885923337866…67140363351006169599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.189 Γ— 10⁹⁡(96-digit number)
31894090885923337866…67140363351006169601
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
6.378 Γ— 10⁹⁡(96-digit number)
63788181771846675733…34280726702012339199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.378 Γ— 10⁹⁡(96-digit number)
63788181771846675733…34280726702012339201
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
1.275 Γ— 10⁹⁢(97-digit number)
12757636354369335146…68561453404024678399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.275 Γ— 10⁹⁢(97-digit number)
12757636354369335146…68561453404024678401
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
2.551 Γ— 10⁹⁢(97-digit number)
25515272708738670293…37122906808049356799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.551 Γ— 10⁹⁢(97-digit number)
25515272708738670293…37122906808049356801
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:57,697,913 XPMΒ·at block #6,806,726 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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