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Block #1,403,304

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2016, 5:48:44 PM Β· Difficulty 10.8058 Β· 5,435,946 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f1b98a64d9ee9c939879d9df8c4746c9bd84d0846e2b79ca1aca64870ad30d97
View on Chainz β†—

Height

#1,403,304

Difficulty

10.805757

Transactions

2

Size

1.14 KB

Version

2

Bits

0ace4614

Nonce

551,617,655

Timestamp

1/7/2016, 5:48:44 PM

Confirmations

5,435,946

Mined by

⛏️ P2SHAXieqr3h7EBaVwa4u5Z89FRm49KKX12v2f

Merkle Root

c2829bd6c4631563a899051296038ebb2f9ffca71dd962089e2b396727b8c85b
Transactions (2)
Coinbaseb7e34febf3a769…6b1add9d05ba6e
1 in β†’ 1 out8.6100 XPM109 B
AXieqr3h…KKX12v2f
d5e43dcead9a99…60e31ee79cd2d7
6 in β†’ 2 out773.4700 XPM966 B
AVpJbiVd…f3No8Y5fAZDBnTpQ…4dRynFqs
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.

2.067 Γ— 10⁹⁢(97-digit number)
20678736533059788921…63600417913418705919
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
2.067 Γ— 10⁹⁢(97-digit number)
20678736533059788921…63600417913418705919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.067 Γ— 10⁹⁢(97-digit number)
20678736533059788921…63600417913418705921
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
4.135 Γ— 10⁹⁢(97-digit number)
41357473066119577842…27200835826837411839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.135 Γ— 10⁹⁢(97-digit number)
41357473066119577842…27200835826837411841
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
8.271 Γ— 10⁹⁢(97-digit number)
82714946132239155685…54401671653674823679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.271 Γ— 10⁹⁢(97-digit number)
82714946132239155685…54401671653674823681
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
1.654 Γ— 10⁹⁷(98-digit number)
16542989226447831137…08803343307349647359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.654 Γ— 10⁹⁷(98-digit number)
16542989226447831137…08803343307349647361
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
3.308 Γ— 10⁹⁷(98-digit number)
33085978452895662274…17606686614699294719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.308 Γ— 10⁹⁷(98-digit number)
33085978452895662274…17606686614699294721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.617 Γ— 10⁹⁷(98-digit number)
66171956905791324548…35213373229398589439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,958,282 XPMΒ·at block #6,839,249 Β· updates every 60s
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