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Block #618,930

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/6/2014, 2:13:43 AM Β· Difficulty 10.9465 Β· 6,214,562 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fb184976ef6d33a8e5cb41603022db2145ed840683910e4619e61be139b84527
View on Chainz β†—

Height

#618,930

Difficulty

10.946495

Transactions

2

Size

434 B

Version

2

Bits

0af24d86

Nonce

1,129,280,730

Timestamp

7/6/2014, 2:13:43 AM

Confirmations

6,214,562

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6ad401173b8ac86afaa809ea9ef458f475c74af597a547c5bc6637678df30e1a
Transactions (2)
Coinbasebc8d862eaa190f…e0f2be11ce35b6
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
042d7c201c3e15…21ec4ce42c2bc8
1 in β†’ 2 out7.1830 XPM227 B
AaACyj3K…Sx9ppKPUARZ9Susn…38kHXmQ1
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.

1.955 Γ— 10⁹⁷(98-digit number)
19555926902629218326…67278534111844260619
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
1.955 Γ— 10⁹⁷(98-digit number)
19555926902629218326…67278534111844260619
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.955 Γ— 10⁹⁷(98-digit number)
19555926902629218326…67278534111844260621
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
3.911 Γ— 10⁹⁷(98-digit number)
39111853805258436652…34557068223688521239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.911 Γ— 10⁹⁷(98-digit number)
39111853805258436652…34557068223688521241
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
7.822 Γ— 10⁹⁷(98-digit number)
78223707610516873305…69114136447377042479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.822 Γ— 10⁹⁷(98-digit number)
78223707610516873305…69114136447377042481
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
1.564 Γ— 10⁹⁸(99-digit number)
15644741522103374661…38228272894754084959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.564 Γ— 10⁹⁸(99-digit number)
15644741522103374661…38228272894754084961
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
3.128 Γ— 10⁹⁸(99-digit number)
31289483044206749322…76456545789508169919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.128 Γ— 10⁹⁸(99-digit number)
31289483044206749322…76456545789508169921
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:57,912,142 XPMΒ·at block #6,833,491 Β· updates every 60s
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