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Block #842,758

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2014, 9:09:10 PM Β· Difficulty 10.9735 Β· 5,997,146 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6f2ad702f6aa4b3d27226e6a9f350770bebac75482381be52bc2f3612e4b2e62
View on Chainz β†—

Height

#842,758

Difficulty

10.973533

Transactions

2

Size

728 B

Version

2

Bits

0af93974

Nonce

214,383,070

Timestamp

12/6/2014, 9:09:10 PM

Confirmations

5,997,146

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

04fa0caf8bbd7de472ce648d76c7e000c279ddd2d984594c571516754952123c
Transactions (2)
Coinbase13edfd7ac1fe04…88db08a3728906
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
7c339f77bd72b7…d70eff535db377
3 in β†’ 2 out11.3907 XPM521 B
AcqLzLhA…eE6LSgnWAcZqa1Y1…oegMFVFR
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.

1.173 Γ— 10⁹⁷(98-digit number)
11733997166926223078…79820124985506559359
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
1.173 Γ— 10⁹⁷(98-digit number)
11733997166926223078…79820124985506559359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.173 Γ— 10⁹⁷(98-digit number)
11733997166926223078…79820124985506559361
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
2.346 Γ— 10⁹⁷(98-digit number)
23467994333852446157…59640249971013118719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.346 Γ— 10⁹⁷(98-digit number)
23467994333852446157…59640249971013118721
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
4.693 Γ— 10⁹⁷(98-digit number)
46935988667704892314…19280499942026237439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.693 Γ— 10⁹⁷(98-digit number)
46935988667704892314…19280499942026237441
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
9.387 Γ— 10⁹⁷(98-digit number)
93871977335409784628…38560999884052474879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.387 Γ— 10⁹⁷(98-digit number)
93871977335409784628…38560999884052474881
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
1.877 Γ— 10⁹⁸(99-digit number)
18774395467081956925…77121999768104949759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.877 Γ— 10⁹⁸(99-digit number)
18774395467081956925…77121999768104949761
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:57,963,530 XPMΒ·at block #6,839,903 Β· updates every 60s
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