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Block #2,459,985

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/6/2018, 9:06:22 AM Β· Difficulty 10.9547 Β· 4,354,476 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27c5db42cd831f42be59787280fca5445e9bfde0d7475b99fc9a7e928885211a
View on Chainz β†—

Height

#2,459,985

Difficulty

10.954723

Transactions

2

Size

722 B

Version

2

Bits

0af468c1

Nonce

136,285,796

Timestamp

1/6/2018, 9:06:22 AM

Confirmations

4,354,476

Mined by

⛏️ P2SHATQq4jFMCXzzWCzRLogsCQY615x9i2mVWz

Merkle Root

a2062199faee02a2720c599a74c0f4f7d34371582e558df9df1bf877d9c4b0d0
Transactions (2)
Coinbasec14dd714ed081a…5a8e2f429085d6
1 in β†’ 1 out8.3400 XPM109 B
ATQq4jFM…x9i2mVWz
bee9643dba24ad…53fd59c80b01e6
3 in β†’ 2 out243.9789 XPM523 B
AJ1wcjJw…dSLbnwjTAciFt7aX…Mes3XESv
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.

1.126 Γ— 10⁹⁡(96-digit number)
11263994404087716857…10580088546959442559
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
1.126 Γ— 10⁹⁡(96-digit number)
11263994404087716857…10580088546959442559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.126 Γ— 10⁹⁡(96-digit number)
11263994404087716857…10580088546959442561
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
2.252 Γ— 10⁹⁡(96-digit number)
22527988808175433715…21160177093918885119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.252 Γ— 10⁹⁡(96-digit number)
22527988808175433715…21160177093918885121
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
4.505 Γ— 10⁹⁡(96-digit number)
45055977616350867430…42320354187837770239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.505 Γ— 10⁹⁡(96-digit number)
45055977616350867430…42320354187837770241
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
9.011 Γ— 10⁹⁡(96-digit number)
90111955232701734860…84640708375675540479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.011 Γ— 10⁹⁡(96-digit number)
90111955232701734860…84640708375675540481
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
1.802 Γ— 10⁹⁢(97-digit number)
18022391046540346972…69281416751351080959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.802 Γ— 10⁹⁢(97-digit number)
18022391046540346972…69281416751351080961
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
3.604 Γ— 10⁹⁢(97-digit number)
36044782093080693944…38562833502702161919
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:57,759,760 XPMΒ·at block #6,814,460 Β· updates every 60s
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