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Block #364,211

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/17/2014, 10:19:06 PM Β· Difficulty 10.4199 Β· 6,443,730 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e28a98aa104704cd1c09a2c741aa2d40a22547e6c886b7254ee34d3503edb0b4
View on Chainz β†—

Height

#364,211

Difficulty

10.419879

Transactions

1

Size

231 B

Version

2

Bits

0a6b7d2a

Nonce

5,959

Timestamp

1/17/2014, 10:19:06 PM

Confirmations

6,443,730

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

6184de10a8bf0483241c31b709ab8498073f442c458e8487e65e09a471cb9443
Transactions (1)
Coinbase6184de10a8bf04…5e09a471cb9443
1 in β†’ 2 out9.2000 XPM137 B
ARmAMwyu…P7Kn74ZTAbiw8n3q…ZnZfgvQW
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.

1.176 Γ— 10¹⁰⁴(105-digit number)
11764798303278117120…56625319853670799359
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
1.176 Γ— 10¹⁰⁴(105-digit number)
11764798303278117120…56625319853670799359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.176 Γ— 10¹⁰⁴(105-digit number)
11764798303278117120…56625319853670799361
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
2.352 Γ— 10¹⁰⁴(105-digit number)
23529596606556234241…13250639707341598719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.352 Γ— 10¹⁰⁴(105-digit number)
23529596606556234241…13250639707341598721
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
4.705 Γ— 10¹⁰⁴(105-digit number)
47059193213112468483…26501279414683197439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.705 Γ— 10¹⁰⁴(105-digit number)
47059193213112468483…26501279414683197441
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
9.411 Γ— 10¹⁰⁴(105-digit number)
94118386426224936966…53002558829366394879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.411 Γ— 10¹⁰⁴(105-digit number)
94118386426224936966…53002558829366394881
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
1.882 Γ— 10¹⁰⁡(106-digit number)
18823677285244987393…06005117658732789759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.882 Γ— 10¹⁰⁡(106-digit number)
18823677285244987393…06005117658732789761
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:57,707,567 XPMΒ·at block #6,807,940 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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