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Block #843,484

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/7/2014, 10:25:37 AM Β· Difficulty 10.9732 Β· 5,998,181 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c3bc5bf245a373dafe4e9c2a6b6dd554386c2bf077ad71905ff641b81e069782
View on Chainz β†—

Height

#843,484

Difficulty

10.973180

Transactions

2

Size

695 B

Version

2

Bits

0af92253

Nonce

2,185,792,770

Timestamp

12/7/2014, 10:25:37 AM

Confirmations

5,998,181

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fb4c36debadc96c48e4a566b22ee0af53d8d80969b806476eac5630cb9783d8e
Transactions (2)
Coinbased9bfcb0a2bb291…dba032c40cb224
1 in β†’ 1 out8.3098 XPM116 B
ANSXnLY2…Sd25TjkD
386857afc6fdb1…c1da9920ca59f3
3 in β†’ 1 out0.0107 XPM487 B
AX4kM81Z…tjaCNqcX
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.

1.675 Γ— 10⁹⁹(100-digit number)
16757753806171428106…91769919162778501119
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
1.675 Γ— 10⁹⁹(100-digit number)
16757753806171428106…91769919162778501119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.675 Γ— 10⁹⁹(100-digit number)
16757753806171428106…91769919162778501121
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
3.351 Γ— 10⁹⁹(100-digit number)
33515507612342856212…83539838325557002239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.351 Γ— 10⁹⁹(100-digit number)
33515507612342856212…83539838325557002241
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
6.703 Γ— 10⁹⁹(100-digit number)
67031015224685712424…67079676651114004479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.703 Γ— 10⁹⁹(100-digit number)
67031015224685712424…67079676651114004481
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
1.340 Γ— 10¹⁰⁰(101-digit number)
13406203044937142484…34159353302228008959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.340 Γ— 10¹⁰⁰(101-digit number)
13406203044937142484…34159353302228008961
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
2.681 Γ— 10¹⁰⁰(101-digit number)
26812406089874284969…68318706604456017919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.681 Γ— 10¹⁰⁰(101-digit number)
26812406089874284969…68318706604456017921
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:57,977,709 XPMΒ·at block #6,841,664 Β· updates every 60s
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