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Block #854,064

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 12/15/2014, 8:16:34 AM Β· Difficulty 10.9689 Β· 5,955,728 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a627da0c7d917c05b9ec525664f6781cdff11bddd44ce7a4bf16b991190441f9
View on Chainz β†—

Height

#854,064

Difficulty

10.968869

Transactions

3

Size

658 B

Version

2

Bits

0af807c6

Nonce

534,588,369

Timestamp

12/15/2014, 8:16:34 AM

Confirmations

5,955,728

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

457f3426dd58712ed2704f22368fcad82fa2f7a9c62dab4014a9e86a04c6445b
Transactions (3)
Coinbaseaa26c89f739ffa…542943843dda9c
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
008fa925ae7281…2b2aa1a00f0211
1 in β†’ 2 out8.2800 XPM226 B
AGs7wuJ6…jjs9LXNFAHRoBSh4…BSVTQ36Q
2a9b31f5ca3834…b64eaa6b6a00f9
1 in β†’ 2 out8.2800 XPM226 B
ALKxid8G…k1xud3HcAS3YRPiP…Qo9e36z6
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.

4.061 Γ— 10⁹⁴(95-digit number)
40610212023325006238…43966985141703346959
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
4.061 Γ— 10⁹⁴(95-digit number)
40610212023325006238…43966985141703346959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.061 Γ— 10⁹⁴(95-digit number)
40610212023325006238…43966985141703346961
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
8.122 Γ— 10⁹⁴(95-digit number)
81220424046650012477…87933970283406693919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.122 Γ— 10⁹⁴(95-digit number)
81220424046650012477…87933970283406693921
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
1.624 Γ— 10⁹⁡(96-digit number)
16244084809330002495…75867940566813387839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.624 Γ— 10⁹⁡(96-digit number)
16244084809330002495…75867940566813387841
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
3.248 Γ— 10⁹⁡(96-digit number)
32488169618660004990…51735881133626775679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.248 Γ— 10⁹⁡(96-digit number)
32488169618660004990…51735881133626775681
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
6.497 Γ— 10⁹⁡(96-digit number)
64976339237320009981…03471762267253551359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.497 Γ— 10⁹⁡(96-digit number)
64976339237320009981…03471762267253551361
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
1.299 Γ— 10⁹⁢(97-digit number)
12995267847464001996…06943524534507102719
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.299 Γ— 10⁹⁢(97-digit number)
12995267847464001996…06943524534507102721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,722,416 XPMΒ·at block #6,809,791 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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